Typically, a "signature" means a "digital signature" which isn't just an image of what you sign on paper. It's an electronic file that is a legal certification that it is you signing the file.
Basically, a scanned image of your signature isn't legally binding whatsoever since anyone can get ahold of something you signed, scan it and say that you signed it.
But if that's what you need, scan your signature and you can create a custom stamp.
Edit: Ooops. Forgot I was in the Reader forum rather than the Acrobat forum.
If you are only using Reader, you cannot create a custom stamp (you need Acrobat). Even if you could, the document would have to be created in a way where you could use a stamp and also would have to be specially enabled so that you could save the file after inserting this stamp. Sorry if I created any confusion.
I have software that does this. Because I feel it may be inappropriate to specifically advertise or push a product in a public forum, I won't mention it here, except to say that my e-mail address is visible (for a time anyway)
I hope the moderators don't mind - and I humbly beg forgiveness if they do, but what I have solves this problem very well (this is what it was built to do) and I think in the spirit of helping you out I may be granted a little leeway ?
If you are developing a product - I may be able to help out in a big way. If not - I will say that this is very much a non-trivial problem, but can be done and I can give you some starting points.