Hi Kinnarid,
Adobe Reader should help you signing the pdf document. But before that you need to check whether document security allows you to "Sign" the document or not?
Open document >right click "Document Properties">Security>Signing
2- Or try "Sign Out" and "Sign In" in the application. Open Adobe Reader>Click [Name at upper right corner]>Sign Out.
Related Help document- Signing PDFs
3- Close the application completely and reopen it, as there's also a possibility when you select the "Digital Sign" under Certificates it becomes grade out until you don't drag the mouse and create a signer box on the document.
Hope this helps.
Regards,
Akanchha