You can not use Adobe Reader to get signing functionality but you can use Adobe Acrobat XI Pro to Extend the forms abilities to allow Adobe Reader users to Sign.
Process to Extend the Form document's features with an existing Signature Field in the Form:
2. Click "Save Now" button
3. Save the file to a new name because you want to keep the ability to edit the file that you were working on just in case you need to make changes later.