Q. Can you give an aliya to a mute individual?

A. Poskim rule that a mute should not be given an aliya since he cannot recite the brochos. Keren Ledovid 27, Shevet Halevy 7: 20, Yad Bekrias Hatorah 24: 3.)
However, Pri Megadim (M.Z. 140: 2) is lenient on the case of a distinguished and honourable leader of the generation, in that someone else should recite the brocho for his sake, and he will comply as “shomea keone.”
Poskim write that even if he is able to communicate by moving his lips, he should not be called to the Torah reading, since he cannot recite the brocho (Minchas Shlomo 1: 34, see also Tefilo Kehilchoso 8: n. 81)
Horav Shlomo Miller’s Shlit”a opinion is similar. However, he added that if the mute can express vocal sounds that his likewise stricken companions familiar with him would understand, it is considered enough of a verbal language for receiving an aliya.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a