Cicero was not a Stoic. He's more or less the definitive example of eclecticism, although his time studying with Antiochus of Ascalon marked him formally as an Academic, even though Antiochus was also really an eclectic. Cicero isn't even really all that influenced by Stoicism. Nor would any Stoicism that he had absorbed have likely moved him far from the norm on slavery. While Seneca famously says in Letter 47 that a master should live in friendship with his slaves on the grounds that they are human beings like himself (the famous line "'Servi sunt.' Immo homines. 'Servi sunt ' Immo contubernales. 'Servi sunt.' Immo humiles amici," "'They are slaves.' No, they are men. 'They are slaves.' No, they are comrades. 'They are slaves.' No, they are our unfortunate friends."), his opinion, and that of the Stoics generally, does not greatly contradict the realities of Roman slavery. Seneca protests against the inhumane treatment of slaves, yes on the grounds that they're human beings, but not because human beings deserve not to be mistreated in and of themselves, but because it reflects poorly on us (the readers...I hope nobody is keeping any slaves who's reading this, and if you are go fuck yourself) as masters. The idea is that slaves have the same origins as free men, and therefore it is a disservice to yourself to mistreat them, since you yourself may well suffer the same sort of misfortune. As Seneca responds to the last imagined protest of "They are slaves": "Immo conservi, si cogitaveris tantundem in utrosque licere fortunae," "No, they are our fellow-slaves, if you realize that fortune has the same sway over you and him alive." Man is not entirely master of his own fate, and therefore it is unworthy of an educated person's "prudentia" and "eruditio" (wisdom and learning) to mistreat those against whom Fortune has turned while still expecting different treatment should the same happen in return. This isn't an antislavery narrative, it's one that upholds slavery, and unsurprisingly Seneca elsewhere urges the reader to bear misfortunes, including possible enslavement, with an equal mind, knowing that man cannot entirely control his own fate.
That said, Susan Treggiari has pointed out that the sentiments that Cicero expresses in his letters about slavery are much closer to those of the Stoics than the Aristotelians, although the Academics typically sided with the Stoics on this one anyway. Whereas Aristotle argued that slavery is a natural condition and that therefore there are some people who are naturally inferior and suited to be slaves, the Stoic argument for the equal command of Fortune over all humans meant that while slavery was a condition that was beyond questioning or fighting, and should instead be borne without complaint, nonetheless those who found themselves enslaved were not supposed to be (an important emphasis) mistreated. In several speeches, precisely those writings in which Cicero tends to be generally disparaging of slaves (in contrast with his private views), Cicero points out that it's possible for a slave to rise above his condition and really make something of himself. On the other hand, in a letter to Atticus Cicero also complains that whatever people Caesar enslaves in Britain will be pretty much worthless, since they don't know how to read or play music (he leaves out the obvious: their sole use to the Romans is as laborers). That human chattel was to Cicero a practical commodity, a resource that, its high value aside, was economically no different than any other, is obvious enough, although Cicero's views on this subject were not exactly outside the norm for his contemporaries. We also know that Cicero had a fairly large number of freedmen, many of whom are named, although we must be cautious given that we don't know how many slaves he had in his household nor what proportion of slaves were manumitted within their masters' lifetime in the households of his contemporaries. He also names an unusually large (only because we have so much of Cicero's personal correspondence) number of his own slaves, with one of whom (Tiro) he was good friends and at least one other (Sositheus) he mourned after his death, commenting that his grief might actually be misunderstood as excessive since it was just for a slave. The loyalty of a particular group of slaves, his litter-bearers when Antony's agents came to execute him, is famous.
Yet Treggiari notes that the picture is misleading. Cicero does not, for example, ever once name or even mention his common laborer slaves. There is a sole exception, a slave that Cicero manumitted but whom he dismissed as a mere "operarius homo" (a workman). This man's name is not mentioned, nor is there any record of Cicero ever freeing any of his other common laborers (though it seems likely enough that he did). All his other slaves and freedmen are high-level house slaves, mostly well educated, and they are the only ones who get mentioned. The rest of the household is faceless in his correspondence, and nameless--indeed, they are without bodies, since their actual presence is never mentioned at all.
It is also clear that while Cicero's educated house slaves were often not enslaved for very long, that manumission was conditional. To become manumitted a man (all of Cicero's known freedpeople are men) had to show not only culture and erudition, but loyalty to Cicero, as he told his wife in one letter, advising her to do the same. That loyalty had to continue past the date of manumission as well. In Att. 1.12 Cicero complains about a freedman of his named Hilarus, an accountant, who had been tasked with Antonius Hybrida to bring some money that had been extorted from the provincials in Macedonia to his former master. Cicero wanted no part of it and denied knowing anything about it, and branded Hilarus to Atticus as a "sane nequam homo," a "wholly worthless fellow." He appears to have cut Hilarus off from himself. He complains about another freedman named Chrysippus in another letter, Att. 7.2. Chrysippus apparently ran away from whatever he was supposed to be doing (Cicero does not explain). Cicero lists a number of offenses that he's not too bothered by, but is especially bothered that Chrysippus betrayed his trust and abandoned his post, which is such a serious offense to Cicero that he considers even re-enslaving him. Chrysippus, like Hilarus, is never mentioned again. Other freedmen, those more in line with Cicero's trust, fared significantly better--the list of Cicero's favored freedmen is much longer, and there are more examples of a more kindly attitude towards them.
Treggiari's conclusion was that Cicero's status as a master was complicated. To a select few of his slaves and freedmen he was quite kind, and he seems not to have mistreated the majority, but to those that he felt had betrayed his trust he had little sympathy, though we are never told by any source that Cicero beat his slaves or anything like that (the threat of re-enslavement is serious, though). And Treggiari pointed out that since Cicero did not implicate his freedmen with his political career very much, unlike some of his contemporaries and unlike, most importantly, the emperors, his freedmen appear by and large to have been free to live as individuals. However, lest this seem too close to the "slavery wasn't that bad, it was even good for some slaves with good masters" narrative common among white supremacists and other disreputable characters, it must be underlined that in no way did Cicero or any of his contemporaries see an inconsistency with the idea that slaves did not deserve mistreatment and the fact that slavery existed. That people were enslaved does not appear to have been an issue to anyone in the ancient world--there is no record of such an idea ever appearing in any text that we have. To Cicero apparently it was not an inconsistency to be able to praise Tiro (which he did, often) for his great erudition and friendship as if he were almost an equal while threatening to re-enslave Chrysippus for not doing what he was told. When Cicero mourned Sositheus he mourned a slave, not an equal, and expressed his concern that his excessive grief was unbecoming since the boy was "just" a slave. An uncommon attitude among his contemporaries for sure, in that someone who was "just" a slave would, to many masters, have merited no grief at all, but still the attitude of a member of a slave-owning society who, though no doubt standing well above his contemporaries in the humane treatment of his slaves, nonetheless in none of our surviving writings questioned the institution, as did none of his contemporaries or successors.