You can do this with the 'Convert URLs to Attachments' automation. It will convert file URLs to attachments in Airtable.
It can also be used in bulk for all records in a view, or to process individual records as explained here. This would give you a button you can click in Airtable to convert the URL to an attachment.
💡 Tip: This automation can also convert multiple URLs to attachments at once. Make sure to separate the URLs with commas, semicolons, spaces, or linebreaks, and include whitespace between the URLs and the separator. For example https://yourfirst.url ; https://yoursecond.url
This automation cannot currently convert links to Google Docs.
Setup
Prepare a field containing public, direct file URLs and an attachment field for the downloaded files. A link to a private account page is not a direct file URL.
Create the Convert URLs to Attachments automation in the workspace and base containing your records, then select the correct Table.
Under Setup, set URL Field to the field containing your file URLs. Set Attachments Field to the attachment field where the files should be saved.
Check Processing Behavior and choose how to handle existing output values before running.
Use a view containing one test record first, then run the automation. Open the resulting attachment in Airtable and confirm it is the expected file before processing the rest of your records.