Assuming you mean Republican Rome, yes, to the extent where it's possible to argue that 'populist' politics defined the transition between republic and empire. The politics of the late Republic are typically classified as a struggle between the 'optimates' (politicians broadly concerned with the needs of the senatorial class) and 'populares', who appealed directly to the authority of the people. That said, this divide is somewhat reductive, and there has been an effort to categorise politicians on a broader spectrum.

The best example, unless you count Caesar (who was kind of a special case) was Gnaeus Pompeius Magnus, or Pompey the Great. He was elected to the consulship in 70 BC at the age of thirty-five, in defiance of the norms surrounding such elections. He managed this, rather like the legendary general Gaius Marius, largely on the strength of his military conquests. Marius' tactic of building loyal support among veteran soldiers and the enfranchisement of his conquered citizens would later be adopted by Pompey, Caesar, and eventually Octavian.

Another famous case would be Tiberius and Gaius Gracchus, know as the Gracchi (the two tribunes who Cicero repeatedly uses to justify political assassination), although again their position as 'populares' has come under scrutiny as scholars have looked at the true impact of their agrarian reform.

To be honest I'd argue that Augustus' rise to power in the late Republic revolves almost entirely around populism. He did not hold extreme power, but he held the greatest authority (auctoritas) in Rome, and that was key, because it basically allowed him to get away with a lot as long as it was felt appropriate. One example is that the split between imperial and senatorial provinces was often ignored, and governors in both simply took orders from Augustus. Indeed, part of the reason for the struggles of his immediate successors is simply that they were never able to command the same respect as Augustus, which made it harder to avoid offending the Senate.

I haven't even mentioned Cicero, who could be seen as a 'right-wing' populist in his own right...

If you want more detail, the popular sourcebook for this period is I believe still Scullard's From the Gracchi to Nero; the use of the Gracchi in the title should tell you how important populism was to the period. There's also Syme's hugely influential The Roman Revolution.