No, he was a minister.
According to his website,
"A false rumor claims that Fred Rogers was once a U.S. military sniper in the Vietnam War. The rumor appeared on the Internet in 1994 and re-emerged several times over the next ten years, most notably after his death in 2003.[44][45] However, Rogers never served in any military force. Beginning in 1963, Rogers developed the Mister Rogers program for the Canadian Broadcasting Corporation. In 1966, he moved back to Pittsburgh, Pennsylvania in the U.S. where he produced Mister Rogers' Neighborhood through the height of U.S. military involvement in Vietnam. Related rumors claim that Rogers had a number of military tattoos, but these rumors are also entirely false."