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Surely.

I didn't necessarily mean a free-standing object that was anchored at only the base.

Another commenter pointed out a project very similar to what I was thinking: StarTram: https://en.wikipedia.org/wiki/StarTram

It has supports and launches the vehicle using maglev; basically a big, tangential, spaceship cannon that launches into orbit using fixed structures.

Heinlein had a similar idea, which he described in The Moon is a Harsh Mistress

The moon also has lower escape velocity than Earth. Lower lunar gravity makes every method of reaching orbit easier.

Looks similar to the "launch loop" concept.