My first thought was that the writer was lying or sitting down and therefore had to reach upwards with his hand to touch her face. Although they could be standing face-to-face and he could still be said to reach up to her face, needing to raise his arm from his side.
However, I looked up the passage and the writer seems to be a little confused. At first he was sitting at a cafe table when the woman came along and he asked her to leave him alone. She left him and "turned the corner". Then he says that he "got up and walked towards this lady…" and:
She looked at me and said, "Will you touch my face?" And for some reason, I did. I reached up and put my hand on her cheek and she started to cry.
But then he writes:
Right there, on the corner with people walking all around, I sat there for a few brief moments with my hand on her cheek.
So he says that he stood up and walked over to her, around the corner presumably, and then says that he was still sitting down. Confusing!
not a teacher