Brink, 24, is a college student and bikini model from Texas.
The unmarried Memphis democrat responded to the young woman twice.
He first tweeted, "@victoria_brink pleased [you are] watching. ilu."
He then tweeted, "@victoria_brink nice to know you were watchin SOTU(state of the union). [Happy Valentine's] beautiful girl. ilu."
Both messages were tagged with "ilu," meaning "I love you," and both were deleted within minutes of being tweeted.
However, Politwoops, a site dedicated to digging up the deleted tweets of lawmakers, showed every tweeted and deleted character.
Tuesday's tweets were not the first online exchange between the two.
On August 27, Brink wished Cohen well on his trips. On May 24, she sent him "happy birthday" messages.
The most recent tweets generated several national news stories and comments.
The Tennessee Republican Party was quick to respond.
In a written statement, Executive Director Brent Leatherwood said, "It is very disappointing that Rep. Cohen would use his official Congressional Twitter account, which taxpaying constituents rely on for news and updates from their congressman, to send personal and unnecessarily revealing messages to college co-eds."
Nashville's News 2 reached out to Rep. Cohen.
He declined a request for an interview; but Press Secretary Michael Pagan said Brink is a longtime family friend and the message was meant to be private.
He added that Cohen has a longtime girlfriend in Memphis.