The twinkling of stars is a phenomenon observed due to atmospheric refraction.

The physical conditions of the atmosphere do not remain constant and so, the refractive index of the air continuously changes.

This leads to continuous change in the direction of the light coming from starsas the changing indexes leads to different extents of bending of light.

Due to this, the amount of light entering our eye continuously changes leading to our perception that the star sometimes appears brighter and sometimes fainter, I.e., twinkling.

Now, we can understand the phenomenon with respect to planets.

Planets are extended sources of light, i.e., they can be thought of as a combination of many point sources of light.

So, every beam of light coming from each of the comprising point sources experiences different extents of bending.

But, what happens is that the extent of bending of all the rays combined averages out to zero.

So, they do not twinkle.