Photograph it flat and bright
Even lighting on white paper gives high contrast, and high contrast survives heavy compression much better than a grey, shadowed scan.
Resize a signature to 10 KB
10 KB is the tightest signature limit forms ask for. Cropping close to the strokes before compressing is what keeps it legible at this size.
Keeping a signature readable at small sizes
Crop to the strokes
Every millimetre of blank paper costs bytes. Crop right up to the signature so the size budget is spent on the ink.
Export as JPG
Almost every portal expects JPG. It also reaches small targets with fewer artefacts than PNG for a scanned image.