Donner de l’effet (à la balle, la boule ou la bille) would probably be the most natural translation.
To be more precise one can use “donner un effet de rotation”. The result would be une balle qui a de l’effet, beaucoup d’effet, etc.

Physicists could also use “donner du moment”, but this would not be understood by laymen.

• The spin the ball has¹ is “l’effet (qu’elle a)”. “Giving it spin” is as Stéphane mentions “(lui) donner de l’effet”.

• If you’re saying the ball spins, you’ll say “(elle) tourne”, from the verb “tourner”. For a wheel, the spin, as a noun, will be “un tour”.

¹ If that’s correct English wording, which I slightly doubt.