My rooster's foot is very swollen and there is no evident external damage.

[centrarchid]

I see signs of what can cause bumble foot.

 

[Wyorp Rock]

Can you clean his feet up really well, be sure to spread the foot pad apart and clean out those nooks and crannies. Do you use paper for your bedding?

Both his feet look swollen to me. On the one foot, there is a yellowish patch, what it that? Look at my circles and arrows.
I agree, he has Scaly Leg Mites.

I would soak the feet in epsom salts, clean off the feet the best you can, you may need to repeat for a few days to get them really clean. Inspect well for any soft spots, infection, scabs, sore places, etc. Keep him on clean dry bedding. I would probably cage him until the feet heal, especially if it's wet outside. You can put him in the cage in your coop if you have room. Apply oil of choice or even triple antibiotic ointment under the scales and on any scabs.
Of course, we want more photos, when you get that debris cleaned off his feet

 

[Gray Farms]

If he is 7 years old and had a broken leg previously, @Eggcessive may be onto something with arthritis.

 

[Eggcessive]

Can you get a good picture of both of his feet and legs together to see if both are swollen? Pictures of the cleaned up foot pads would also be good. If both feet are swollen, there could be a possibility of gout. If you have a good relationship with your vet, you might be able to get a prescription drug meloxicam, for pain and inflammation. But many use aspirin which you could give orally 81 mg low dose once in the morning, and once in the evening. Or use 325 mg per each 8 ounces (240 ml) of water.

 

[WindingRoad]

The redness sure shouts INFECTION of some sort. Did he get splinter or something that pierced the skin. Just throwing out suggestions questions here. Ever hear of Bag Balm. Great stuff. Google for the scoop on it. I use it for everything. Pulled out a hangnail the other day on my thumb. Bled pretty bad. Washed with soapy water and put bag balm on it with bandaid. All healed up now. I'd continue soaks and maybe try to express (squeeze out) any gunk. Then use BB or other topical antibiotic and warp to keep as clean as you can. Another helpful idea is to put him in a chicken sling in a tub. That way he can't walk through his poop and contaminate it again. KWIM.. Good luck and keep a close eye on that.