Not possible because you need a phono amp.
The cheapest way would be to find an old receiver with a phono input. You could probably pick one up at a garage sale or charitable type thrift store for cheap.
Of course sense it's a an USB turntable, you can hook it up your computer, plug in the speakers to computer. Assuming that the PC speakers have built in amps which they most likely do have amps.
Most basic way is you still need something to boost the output of turntable via a receiver(or a basic phono amp) to then connect to the speakers. A rca adapter won't work.
Happy listening, the Prisoner