Can an object moving at a constant speed have acceleration?

Acceleration is defined as the change in velocity over a given time period. Velocity is a vector quantity: it includes speed and direction.

That being said, you can accelerate an object without changing its speed by simply changing its direction.

A body moving along the circumference of a circle its speed may remain a constant, but its velocity will not be a constant since its direction of motion continuously changes, since the velocity changes it has an acceleration.