Archaeologists have taken samples from perfume bottles and identified chemical makeup of perfumes, so there are studies that show what they were made of. This open access project for archeological chemistry might have relevant projects/bibliography, though they aren't limited to perfumes. Some archaeologists and scientists have recreated perfumes based on these tests and some museums have done projects for visitors, but as far as I can find none are commercially available. I did find this blog post by the Getty Villa, a top museum, that describes a workshop they did for recreating ancient perfume and describes how it can be done.

I will say, the perfumes would not have been like we are used to today. The Getty interactive sums it up well with its title of "Spicy Scents." Perfumes were made with a much thicker based, like olive oil, and were much more pungent so that they would be long-lasting and cut through the much-smellier ancient world.