There's no direct option for inserting a signature in Google Docs, but you can easily insert a signature as a "Drawing" in Google Docs.
Open drawing editor
- Go to Insert.
- Choose Drawing.
- Select New +.
Choose to draw with a scribble line
- Open the line type selector (shown above).
- Choose Scribble.
Draw your signature
Carefully draw your signature, using the scribble line editor. Note that when you release your mouse, the line will end. It's useful to craft your signature in stages, so you can go back and redo your work if need be.
Save and close
Click Save and Close when finished.
Once the signature is inserted, it's likely to be too large for your document. You'll need to click on the signature and drag the blue box to resize the signature in Google Docs.
Hint: If you plan to use your signature in Google Docs a lot, then you should be sure to save this somewhere easy to access in Google Drive. Then, when you need the signature again, you can just open this document and copy and paste it into the new one.