There is no good evidence that he ever did.

Tesla made various claims about his earthquake machine, but these claims were made many years after the incident was supposed to have happened. There are no corroborating witnesses, no media accounts, and the USGS seismological records of the time and place the earthquake was alleged to have happened show nothing out of the ordinary.

How did Mr. Tesla make a small machine that caused an earthquake? Is it an experiment for AC?

He didn’t -

And he didn’t shake a building either -

There are natural frequencies but there are also damping effects

You CAN shake a building so it resonates but you need to input a LOT of energy - nothing that I would call a “small machine” would do that