A generalized analysis of rotational symmetry in quantum mechanics is presented for a charged particle moving in the field of a magnetic monopole. The generalized orbital angular momentum is obtained，which is the same as that obtained previously by a different method. The transformation of the wave function under rotation contains an extra phase factor compared with the ordinary case without the magnetic monopole field. The explicit expression for this phase factor is worked out. The familiar quantization condition for electric charge is obtained by requiring the phase factor to be ±1 under a rotation of angle 2π.