Breast bands and other kinds of support were used. The history of the corset as we know it, however, begins in the 1600's, according to Wikipedia. I find this hard to believe. Perhaps this is because whalebone was used in medieval and baroque corsets, so, the way we see it today, anything that does not have whalebone in it is not really a corset? The Romans did hunt whales, but maybe not enough to make whalebone sufficiently affordable for corset making. I'm kind of stumped here.
I suspect the short answer to this is that we do not know for sure. The reason for this is that the evidence we have for what the romans wore is not their actual physical clothes as over the period of time i doubt if any roman clothing intact has survived as throughout human history until industrialisation clothing was handmade and so expensive (relatively) and usually worn until it literally fell to pieces. We do have scraps and fragments (see here). So the evidence for clothes is usually statues, mosaics and any wall paintings that survive such as those at Pompei of Herculaneum as well as any writing on the subject that survives. The case against was that Roman clothing was quite simple and sophisticated tailoring was not employed so the construction of a corset as such is unlikely. It is possible that individuals may have "bound" themselves with bandages as rudimentary device, but they would then hardly have this made into a statue to put in a public place. The only possible source of material could be Roman erotic art, of which there is a lot although some of it still partially suppressed where you are seeing the Romans at leisure but this does not appear to yield corsetry.
Edit:- Someone has commented that i did not really answer the question but pointed to sources which is correct. At a distance of 2,000 years it would be hard to produce a definitive answer as evidence may yet be uncovered that would extend knowledge and reverse opinions.
However if i had to give an answer then i would say no, Roman women did not wear corsets. From all the evidence that we currently have in statues, writings, drawings, paintings, mosaics, graffiti etc. there is nothing to indicate a garment that was like a modern or victorian corset. It is also the case that Roman attitudes towards clothes and clothing, the state of tailoring and engineering would not lend themselves to the manufacture of such a garment. And before someone tells me the Romans were brilliant engineers then yes they but a corset is not an aqueduct, or a ballistae or poured concrete