Can I put my website in the signature beneath posts?

Can I put my website in the signature beneath posts?
It is a business site.

Depends !

If it is a spammy link you will get nailed for it.
Try it and see.
Worst case somebody reports it and the link gets pulled.

I see some people with links in the section where you have the text "Hey! I'm more of a wannabe than an electrical engineer right now..."

...R