Use GIMP. Open your file. If it's not RGB, change the mode to RGB (=Image > Mode > RGB).
Insert alpha channel, if it does not already exist. Goto Layer > Transparency. Option "Add alpha channel" is grayed, if there's already one.
Increase the contrast with Color > Curves so that paper is full white. Adjust the hue and saturation of the writing good after the paper is white. Do it with Colors > Hue-Saturation. Be sure you do not make the background grey.
You should have a single layer image:
(the text here is random jumble scratched with the mouse, it's not readable writing in any language)
Then set the current foreground drawing color to white and apply Color > Color to alpha. White changes to transparency:
Then export your image as PNG. It may be a good idea at first check it has the right print size and resolution (300dpi). For it goto Image > Print Size.