Question

In order for an object to have a centripetal acceleration, what must be applied to the object? 

Answer 1

In order for an object to have a centripetal acceleration the force must be applied to the object. Moreover, this force should make some angle with the vector of current velocity of the object. In case when this angle is exactly $90\degree$, an object performs circular motion. In case of any other non zero angle, the tracjectory of the object can be any non linear curve.

Answer. Force that makes some angle with the vector of current velocity.