Simple answer, yes, but setting everything up would be a little more complex.
First you'll need to make sure your existing deck has output other than pre-amp. For example, a deck plugged into an amplifier then take the tape record out from the amp and wire into your PC - this is how I've done it. (By this I mean using an input on your sound card - eg. mic)
You then need some software to record from the source and for this I use SoundForge but there are many other free programs out there. I use this because I can see the waveform on the screen and can easily crop the ends off to remove the bits that I don't want like extended silence. It also allows me to edit the recording like increase the volume.



