To have a face like an angel implies that Stephen’s face was radiant or shining in some way, similar to the face of Moses after he came down from the mountain (Exodus 34:29–35).1 Such a shining face was the result of and confirmation that someone had spent time in the presence of God.2 It is important to remember that the members of the Sanhedrin were the ones who saw that his face was like that of an angel. Even before he began to answer their questions they could see there was something special about this man. Presumably Luke received this information from Paul who was likely present during the trial (Acts 8:1).3
15 And gazing at him, all who sat in the council saw that his face was like the face of an angel.