You'll need to allow pop-ups from Turnitin to use Google Drive upload.
In
If you've made a mistake, use the trash can icon to remove the file.
You can choose to add your submitted files to the account's private repository by checking the Index to your account's repository check box.
This option will not be available if your administrator has opted to store all files in the account's private repository.
Monitor the progress of your upload in the upload progress box at the bottom of the sidebar.
Select Open to view the document or select the file from My Files.
Your Similarity Report may take a few minutes to process after your upload is complete.