Yes, a 50mm lens is good for portraits – but it is intended for full- and medium-length shots, not for close-ups where it will begin to distort facial features.
So, if you are intending to shoot no closer than three-quarter or head-and-torso portraits, check out the best 50mm lenses. For tighter portraits and headshots (and, indeed, full- and medium-length shots as well), an 85mm lens is the best option.