Can I become a partner in a business with a retirement visa ???

Why not? However, you cannot work. You might be able to receive Directors fees though, minus 15% withholding tax.

Sent from my iPad using Thaivisa Connect Thailand

If you are likely to benefit in any way financially from this partnership, it is safest to assume that the answer to your question is "no" IMHO.

You can be an investor in a business, but not actually work in the business. That includes signing paperwork. For that you would need a work permit, which you don't get on a retirement visa.