I'm not aware of any way, at a consumer level, to test for nicotine concentration, specifically.
I'm assuming that you want to test concentration, as you mentioned titrating. Titrating will indicate concentration of organic bases, such as alkaloids, of which nicotine is the major one. It only works on freebased alkaloids, and only if they aren't contaminated with any other acids or bases.
As far as I know, tests designed for detecting nicotine use in humans, actually test for it's metabolite, cotinine. That would not be very useful.
Speaking of testing a dark liquid implies that it's contaminated with flavorings/colorings, or possibly a simple
tobacco extract. Simple extracts can't be titrated anyway, as the alkaloids would likely be mostly in
salt form, and there would be other molecules that skew the pH. Other flavoring or coloring could likely have the same effect.
If you're curious about the nicotine content of a simple
tobacco extraction, expect it to be low, such as in the 1mg/ml range, if it's diluted enough to be vapeable.