I've seen the opposite, i.e. a PC keyboard connected to a Spectrum, but not this way around. An Interface 1 will give you a serial port if terminal-like communication is sufficient, although I suspect you're after a "general purpose" PC-compatible keyboard.
If you're not worried about preserving the Spectrum, it may be possible to wire up a modern keyboard's electronics to the Spectrum's keyboard. Unfortunately I'm not so sure how modern keyboard's membranes are wired and they are probably completely incompatible. You would also be limited by the physical number of keys you have on the Spectrum which may not be practical for anything PC-oriented, although you could get around that to some degree in software on the PC.
The other route is of course what patscc suggested. Unless it has indeed been done before, building such an interface isn't trivial and you'd also need to write some kind of software on the Spectrum to talk to it.