If it's CS6 or CC? Yes.
If it's older, you'll have to buy a new copy.
Mike M wrote:
If it's CS6 or CC? Yes…
If it's CC you're already entitled and able to download and use one version for each platform.
If it's CS6, you can ask for a crossgrade, which goes for "a nominal cost" and entails providing proof of destruction of the Windows version.
Not so 'nominal' from what I have read here previously. In fact someone mentioned half the original cost, or about the same as a single version upgrade, or a year's worth of CC Photography deal subscription.
Heck, what am I talking about. I was thinking $10 a week, but it's a month of course, so four years CC subscription.