Yes, you can definitely import the links from Google Search Console, as well as all the other popular sources, like Majestic, Ahrefs or Moz.
To import your file click "Import links via file upload" icon in the Your Links section:
There will be a popup where you can upload your file.
To import links from other sources, you need to make sure that the imported file matches the format that Monitor Backlinks accepts. You can click on "see examples by clicking here" to see examples of the accepted file formats.