Before you import your video, create a custom 1:1 import video mode preset to use, eg: 640x640. (Settings>Video mode>Custom)
Once you’ve imported your vertical video, use the ‘Rotate’ filter to scale the video to fit the 1:1 space.
If you’re doing this directly in Shotcut, the easiest way I’ve found is to go to Settings > Video Mode and set it to a custom square resolution (like 1080x1080) before importing. Then just use the Size, Position & Rotate filter to fill the frame. Also, if you happen to have any static images or assets you need to prep quickly for the same project without opening an editor, I sometimes use this crop tool just to save time.