To behave misleadingly, esp pretentiously; SHOOT someone A LINE (1934+)
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with put on an act
put on an act
Pretend, especially in order to deceive; also, show off. For example, We were afraid Charlie had hurt himself, but he was just putting on an act, or We know you're a good swimmer—stop putting on an act.
[ c. 1930