Can you fly a plane if you are color blind?

Mostly. A private pilot license does not require that you be color normal. Some commercial applications will restrict the license if you are color deficient and this usually is a ban for flying in the military.
Yes. A pilot in the U.S. Is allowed to fly planes even if he is color blind, but he has 2 restrictions on his license. His license will say "not valid for night flying or by color signal control". Color signal control is when the control tower flashes red, green, or white lights at the pilot to give him instructions when the radios are not working, which rarely happens.