Would it be possible...

[Merovaeus]

to connect a turntable with RCA connectors to a computer and record an LP's contents into a music file?

if so, how would one accomplish this?

 

[anotherguy159]

yes.

 

[mustang_steve]

you need a phono amp, preferably with a RIAA filter to get the proper output level/tonal balance. rat shack used to sell one for about $30.

 

[Mister X]

http://www.pinnaclesys.com/ProductPage.asp?Product_ID=1478&Langue_ID=2

 

[Mister X]

If you can handle a soldering iron this may be of some interest to you....
http://www.maxim-ic.com/appnotes.cfm/appnote_number/1931

I would replace the opamps with something a little better suited for audio use but as it is it SHOULD perform pretty well.
I will let you know after I build it.