He looked me straight in the eye.
I wonder if 'look' can be used as a transitive verb like the sentence above.
We learn 'look' needs 'at': look at something or someone
The usage look someone in the eye is defined in sense B2 Collins Dictionary:
to look someone in the eye or look sb in the face
phrase [VERB inflects]
If you look someone in the eye or look them in the face, you look straight at their eyes in a bold and open way, for example in order to make them realize that you are telling the truth. He could not look her in the eye.
The OP’s example is similar to that and should be fine.
He looked me straight in the eye.
For information, this phrase is also used in several popular songs.