This seems to be taken from Plutarch, but the account of Cleopatra’s ship setting sail with perfume announcing her presence is set in Tarsus (modern day Turkey) not Rome. Here is the passage in question:

She received several letters, both from Antony and from his friends, to summon her, but she took no account of these orders; and at last, as if in mockery of them, she came sailing up the river Cydnus, in a barge with gilded stern and outspread sails of purple, while oars of silver beat time to the music of flutes and fifes and harps. She herself lay all along under a canopy of cloth of gold, dressed as Venus in a picture, and beautiful young boys, like painted Cupids, stood on each side to fan her. Her maids were dressed like sea nymphs and graces, some steering at the rudder, some working at the ropes. The perfumes diffused themselves from the vessel to the shore, which was covered with multitudes, part following the galley up the river on either bank, part running out of the city to see the sight. The market-place was quite emptied, and Antony at last was left alone sitting upon the tribunal; while the word went through all the multitude, that Venus was come to feast with Bacchus, for the common good of Asia.

Now this account is believed to be based on eyewitness stories but Plutarch is known for embellishing his accounts and I can not at the moment recall another primary text which mentions heavy perfume wafting from her ship. This passage does not state that her sails were dipped in perfume however, it just states that a heavy scent of perfume was carried down the river. Additionally, we have no reason to believe that she would have done this when travelling to Rome. In fact, we have shockingly little commentary on her visits to Rome prior to the assassination of Casear. In sharp contrast to on-screen adaptations, it is believed that these were meant to be low-key and inoffensive political excursions to the capital.

Another interesting point is that the association between Cleopatra and perfume is actually a bit more complex than it may first appear. For one thing Egypt was a major producer of perfumes which were known at the time for their variety and luxury. Alexandria, Cleopatra’s capital, was no exception to this and was the site of countless workshops which produced perfume for the Roman Empire for centuries to come. Some ingredients and scents used in Egyptian perfumes originated within Egypt but others were imported from Asia, particularly Arabia and India.

Perfume was associated with makeup and unguents in antiquity but it also held more negative associations with excess, luxury, femininity (which often read as weakness in Graeco-Roman culture) and promiscuity which was associated with all of the above. It is for this reason that the association between the Ptolemies, especially Cleopatra, and perfume is more than a casual observation about Egypt’s cosmetics industry, but also a way for Roman authors to reinforce the idea that they were fabulously wealthy and grossly amoral. Plutarch treats Cleopatra a lot more sympathetically than most Roman authors but he still goes out of his way to paint in a broadly Oriental vignette as a capable, almost masculinely so, woman who was nevertheless afflicted with all the flaws of her sex.

It is not altogether implausible that when Cleopatra went all out in impressing Antony she would have had expensive perfumes wafting from her ship but it could also be true that Plutarch made this bit up to make his story more interesting. It is pretty badass to sail in like what is described and the actual scene was certainly something to marvel at, but not all of the details have to be 100% true.