Sure you can. Most computer have soundcards these days, and most of those have line inputs. Send the taped stuff out your direct outs on each channel, two at a time, while recording on the computer (you'll need a multitrack audio recording application for that). You could also get a multitrack soundcard and record all four tracks at once to a separate track on the computer; that'd be the most straightforward approach.
If possible, record a sharp dry click onto all four tape tracks a couple of seconds before the song starts. This will provide a nice visual reference in the waveform for lining up all four tracks precisely if you do have to do them with a stereo sound card.
