What do you mean the truck is rated for 10,050lbs? You must be referring to its published tow rating because there's no way a Ram 1500 has a GVWR that high.
GVWR is the maximum weight that your truck alone can weigh, and that is one of the numbers you need to consider when selecting tires. I'm willing to bet your truck's GVWR is around 7,000lbs give or take. If that's the case then a tire rated to 2650lbs like you said is more than enough. You must also consider the rear axle weight rating. If your rear axle is rated to 4000lbs then obviously each tire must be 2000lbs rated minimum, for example. All of these weight restrictions are published on a sticker inside your driver's door jamb.
It is always a good idea to over-tire your vehicle. I run Load Range E tires on my truck that are rated for somewhere around 3500lbs each even though my truck maxes out at 7700lbs GVWR. You'll have a much more stable tow, cooler tire temps, and a better resistance to flats. If you shop around and look at different brands you should be able to find your exact tire size in a higher load rating. Heck, even Load Range C or D would be fine with what you're pulling. I always like going up a size or two in tire when I replace and I've noticed barely any speedometer discrepancy.
2013 F-150 EcoBoost MaxTow
2013 Jay Flight 28BHS Elite
"My wheel lugs require more torque than your Honda makes!"