Haven't tried but I think you can do it with Adobe Reader.
Thanks, I just tried that, and it is very cool. I saved a test document from Word as a pdf, emailed it to myself, opened it on my phone in Adobe Reader, and there is a pretty easy and robust signature capability.
First tap on the screen to show the row of icons at the top, then tap on the icon that combines a text balloon with a pen.
Then tap on the icon that appears that looks like a fountain pen.
Then tap on the screen where you want to insert your signature.
A box opens up that says, "Sign Here." Write in your signature. Wait a moment and it will give you the option to "Clear" if you want to start over, or you can press "Save." After you save, it will then insert your signature into the document.
Tap on the signature, and it then gives you the ability to scale and move your signature, as well as adjust the pen thickness, ink color, and opacity.
If you want to add a second person's signature, follow the same steps, but after tapping where you want to insert your signature, choose "Edit Saved Signature" instead of "Add Signature."
When you are all done, it's easy to share the document by whatever method you choose.
Screenshot of two signatures, the first used twice with adjustments to thickness and color:
I had earlier installed an app (can't remember which) to sign pdf's, but it was more complicated and added legends to the document allowing a recipient to verify the signature via the app's web page, etc., way more than I needed. Doing it in Adobe Reader is slick!