"It is distressing, though, to have a president that frankly will tweet and retweet things as juvenile as that", Schiff said on ABC's This Week programme.
Mr Trump has stepped up his criticism of Mrs Clinton since the Democratic presidential nominee re-emerged in the spotlight to promote her new book about the 2016 campaign.
The tweet shows Trump swinging at a golf ball and nailing Hillary right as she walks onto a plane.
He retweeted the GIF, captioned "Donald Trump's wonderful golf swing #CrookedHillary", from the account of a supporter whose profile identifies him as Mike from NY. The GIF clearly splices two different video clips together to make it appear as if the President is hitting a ball right at the former first lady.
White House spokeswomen did not respond to a request for comment. Another presidential Twitter share last month - later deleted - showed a train hitting a person, again with a CNN logo imposed on the figure's head.
Though Trump had been uncharacteristically silent on Twitter as of late, a spate of freaky tweets Sunday morning suggested a return to form for the president's controversial social media tendencies.
"We can not normalize this kind of behavior from the president of the United States", she said.
"The "deplorables" came back to haunt Hillary.They expressed their feelings loud and clear".
It's a big week for President Trump.