Electrical 'input' connector?
Yes, the sort of thing you are looking for exists; you can find them under the name inlet (opposite of outlet). The most commonly seen type is the C14 socket used on computer power supplies, but ones compatible with regular AC extension cords are also available.

(I'm not able to tell you whether using one in this application would be safe or code-compliant, so this doesn't fully address your question, but I hope knowing what it's called will help.)