Can children's benadryl (diphenhydramine) cause an eye twitching tic?

It is possible: If the eye twitching happens soon after giving the medicine (and does not occur at other times), and the child is not taking other meds, it is probably the cause. I would avoid it in the future if possible.

Yes: Benedryl can cause children to exhibit a tic. If you repeat the administration and the tic recurs, speak to your doctor about an alternative.