Open the Word document in the Microsoft Word app on your iPhone
Tap the document to show the toolbar
Tap the Edit icon if needed
Tap the Insert menu
Select Signature or Draw, if available
Use your finger or Apple Pencil to sign directly on the document
Adjust the size and position of the signature
Save the document
If signature tools are not available, export the document to PDF
Open the PDF in Files or Markup
Tap the Markup icon
Tap the plus icon and choose Signature
Create or select your signature
Place the signature on the document
Save the signed file