Can I use double sided tape to install carpet on a concrete floor?
There is a type of very strong double sided tape that you can find at a carpet supply house. However, that would be harder to remove from the floor when you decide to change the carpet (it's very very strong). 

If it were me, I would use a product called "spray tack" also found at carpet supply shop. Or big box stores sell a similar product by 3M, it's just spray adhesive. 

The real deal carpet supply house spray is much better, but either would do the trick. Spray just the floor for a quick bond, or spray the floor and back of carpet for more secure bond. Either way it will be easy to remove when/if you decide to remove it.