Provided the mounting holes/screws line up, you certainly can.
Whether you should is another question altogether though.
When bottom mounted with the fan facing down, it's drawing cool air in, and exhausting out the rear of the PSU - a pretty good idea to assist with longevity of your PSU.
If you orientate the fan facing 'up', it's drawing in warm(ish) air from inside your case - so it's not quite as effective in keeping your PSU cooler (depending how warm it is inside your case).
It's highly unlikely to do any damage at all, but it's just 'better' to have the fan facing down & only handling cool air.
If you're going to be on carpet, what are you planning to put under it?