As a 90% disabled veteran, am I eligible for vaccination now or anytime soon?

On the VA's "Healthy Vet" web site there is a link to signup for Covid-19 information. The VA will announce when they will start vaccinations. So far my VA clinic has completed their planning and is waiting for the vaccine to be distributed.

Yes...ish. I assume you are referring to the COVID vaccine.
VA, just like pretty much everyone else, is working through a priority list. Last I saw they were inviting those who get their health care through VA and 55 years or older to make appointments, at least in the Tennessee Valley area.
Vaccines are supposed to be no-cost, and as a result, I do not think the VA is doing a lot of "screening" to determine if you should be getting it from them, only to determine your priority. My impression is that everyone in health care - VA included - is working to get it out to as many people as possible, as quickly as possible.

Based on your profile picture, I am guessing you are on the younger end of the age spectrum (you look relatively young in a uniform that was only relatively recently adopted...), so unless you have complicating risk factors, I am guessing you will have a bit of a wait.

If you think you may have complicating risk factors, especially if those factors include any kind of respiratory or cardiac condition, I would recommend you reach out to your PCM and discuss your risk and your eligibility to move to the front of the vaccine line. Otherwise, sit tight, we'll get to you eventually.... (FWIW, I am in the same boat... 44 years old with no risk factors.)

Check with your medical provider.

The VA is moving slower then power restoration in Texas. Since each state has differing rules on who can and cannot get the vaccine at this point in time. Some VA's are getting more vaccine than other VA's. Last I heard it was vets over 75 and those who have had organ transplants and certain other conditions.

Thanks for sharing

Your age determines how soon

Initially, the VA (at least the one I'm enrolled with) was doing Veterans 75 and over, or those with conditions that qualify them. As of last Saturday, they started giving them to Vets 65 and older on a no-appointment basis. I got mine and it was EXTREMELY organized and aside from waiting 15 minutes after to ensure no adverse reactions, it took me less than five minutes before I got the shot. I have a March appointment for shot 2.

You will need to have that conversation with your VA and Primary Care team. At my VA compensation percentages aren't being used as a determining factor to who gets the vaccine first. They are using age, any illnesses that mark you as high risk for COVID and they are also moving any medical personnel or first responders to the front of the list. I am 90% as well and I am just waiting for the next phase to go around.