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.