A particle moves in a circular path with a uniform speed. Its motion is
Oscillatory motion is to and fro about a mean position like that of a pendulum or spring mass system. This very clearly isn't oscillation.
SHM is a special case of oscillation. Since it is not oscillation! How on earth can it be simple harmonic?! It's not angular SHM as well because that's oscillatory too.
Now the question is: Is it periodic?
if you take any reference point on the circle on which it is moving and observe the particle you will find it comes back to the same reference point with the same velocity after equal gaps of time. This is what we mean when we say that the motion "repeats” itself.