Strictly speaking he is not a Ranger.
Serve in 75th Ranger Regiment and earn a tan beret and Ranger Scroll (unit patch) = Ranger
Graduate Ranger School and earn the Ranger Tab = Ranger qualified, tabbed, or "graduated Ranger School"
However, this usage is not consistent even in the Army. Much less by campaign staffers or reporters. And I have yet to see anything from Tom Cotton or his campaign literature claiming he served in the 75th Ranger Regiment. He is usually very clear about his service. See for example, the quote RoadKingLarry posted. The only direct evidence I've seen was that campaign flyer stating he "volunteered to be an Army Ranger." That looks like it was written by a campaign staffer or local party with limited knowledge and limited space.
Underneath all the media hype and political accusations I'm not sure he's even guilty of using the term "Ranger" loosely.