Jackie Speier's tweet ends by saying, "Because women have the right to bare arms."
This follows female reporters being removed from certain areas for wearing sleeveless outfits.
Republican Speaker Paul Ryan has urged compliance with the dress code, although he has indicated he will look into the possibility of changing that code.
Men must wear coats and ties as part of the dress code.
In 1993, U.S. Sen. Barbara Mikulski - known as the "Dean of Senate women," according to CNN - wore pants to work, challenging a long-held rule that females must wear skirts on the Senate floor.
"The Senate parliamentarian had looked at the rules to see if it was okay," Mikulski said in a CNN interview. "So, I walk on that day and you would have thought I was walking on the moon. It caused a big stir."
AZ Rep. Martha McSally with some dress code commentary on the House floor a few minutes ago: pic.twitter.com/cierlS75ZC— Alexis Levinson (@alexis_levinson) July 12, 2017