A particle moves in a circular path with a uniform speed. Its motion is

If particle moves at uniform speed) it covers the path of circle in regular interval of time. Hence, it is a periodic motion.

If it is moving with uniform speed the force acting on it will be centripetal force (. And this is inversely proportional to distance of particle from origin. And in SHM the force has to be a type of which does not resemble with it and it does not oscillate about mean position. Hence, it is neither SHM nor oscillatory motion.