If you have anywhere from 10 to 100 thousand US dollars hanging around, sure. If you just buy a GC/FID, GC/TCD et cetera ("simple" analog detectors) it will be on the "lower" end of 40 thou, but will also require pure "standards" of drugs to compare with for 100% certainty. GC/MS will be "starting at" 40k for a used unit. New units are easily 100k.
You'll also need tanks of compressed gases for the GC (high purity H2 or He are the norm), a dual stage vacuum pump for the mass spectrometer, a column suitable for your analysis, area and reagents for sample preparation, and a setup for integrating chromaograms and doing library searches for your MS data. And all the manpower and effort to install and familiarize yourself with the system, troubleshoot it when it breaks or fucks up, and maintain the column, inlets, injectors etc. to provide relaible results.
It is easy to see why there are few non-gov't labs who analyse illicit street drugs. With such a high capital cost, having the premise of the DEA taking all your shit for non-compliance if you ever fuck up has rather chilling effects. Much easier to start a reputable analytical chemistry division, or go into flavours and fragrances or petroleum chemistry or some shit instead, where you can do your analyses without the Feds breathing down your neck.
If you are in a large enough university with a chemistry program, you could see about using a shared GC, some universities have one that people can take turns on. Not too sure that profs would like you testing pills on it though - but you could always frame it as an academic excercise and write a lab paper on it or something?