I have two sites connected by a T1 circuit. Currenlty I have only a single router on both ends, but I would like to add redundantcy, HSRP, GLBP, or simular in case a router fails (see picture). Is this possible since I only have a single T1? Is there anyway that the two routers can connect to a single T1 to provide a redundant interface?
Your main problem is that T1 is point-to-point and you can't terminate it twice, as Ron M. has pointed out. You'd need some kind of hardware switch and set up some router monitoring that toggles the switch.
Depending on the router and line failure rates, it's probably not worth the trouble, as Ron T. has pointed out.
For real redundancy, you'd need a second, independent site-to-site connection and then you can set up failover based on router or line failure.