The 34-year-old defender has been training with the Gers over the past fortnight and played in the 2-1 pre-season friendly win over Charleston Battery during the week.
The Daily Record reported earlier this week that Warburton was unlikely to sign him permanently, and the man himself seemed uncertain when asked about it.
"Yeah he's come in. He's obviously a very experienced player, an international player, but we'll chat to him after this interview and see where we are," he said to Rangers TV.
The former United States centre-back has 69 caps for his country but it remains to be seen if that is enough to see him become a part of one of Scottish football's most exciting projects.
In total, Warburton has signed eight players this summer - Jordan Rossiter, Joey Barton, Clint Hill, Josh Windass, Matt Crooks, Niko Kranjcar, Matt Gilks and Lee Hodson - and there may be one or two more to come in.
One position they need to strengthen is up front, with a 36-year-old Kenny Miller representing Martyn Waghorn's only real competition in the number nine role.
Rangers fans have a huge amount of affection for Miller, but he is very much in the twilight of his career and a younger man may be needed to challenge Waghorn.