You would need a Sonos product with a line in. See the FAQ. 

Is there anyway to transmit the record player via bluetooth or wireless? What sort of line in do you suggest?

Your One doesn’t have Bluetooth input or a Line-in connector.
 

You could Bluetooth to a Roam. 

Gotchya. Can I send the record player to a wifi signal and play it through the sonos app through the One speakers?

If you want to play through the One you’ll need a Sonos device with a Line-in such as the Five. I think you’ll also need the pre-amp to boost the turntable output to a suitable line-in compatible signal. Then use the Group feature to play the TT signal to your choice of speakers/rooms. 

You cannot connect a non-Sonos device tot Sonos via wifi. That’s why, as stated above, you either need a Sonos Port or Five to connect to by cable and get the sound into the Sonos system this way (in your case you’d need a pre-amp too), or use a Roam and a bluetooth transmitter to get the sound from your turntable into the Sonos system (you’d probably need a pre-amp too).

The only other option is a local streaming radio station. Some people on the board have done this.  
 

1. Connect turntable to audio inputs on computer, either a full size or single board like a Pi
2. download and install local streaming audio software
3. stream audio from input using said software
4. Connect to station with local network URL
5. save as favorite

does this option still work today? I’ve never tried it, but have seen it referenced here when this question comes up from time to time. 
 

The other solution goes back to getting a Sonos device with an input, but this is of course more expensive.

https://www.instructables.com/Add-Aux-to-Sonos-Using-Raspberry-Pi/
 

here’s an article on the idea. You still need a preamp - phonograph level won’t be high enough. Are you sure your turntable doesn’t have a preamp built in?

If you can connect the player to a Windows PC then you could use a program called Stream What You Hear to broadcast the output to Sonos