Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
There is no harm Insha Allah for a man to pray in a half-sleeve shirt, as that covers his shoulders. The Prophet (Sallallahu Alaihi wa Sallam) said: "One of you should not pray in a garment which does not cover the shoulders." Since the shirt covers the shoulders, there is no harm in praying in it. However, when performing a prayer, a person should look his best according to his ability.
Allah knows best.