I am not a forensic scientist but sadly I believe the answer to your question is no. There is a technique called DNA fingerprinting that analyzes the different gene sequences in a sample of DNA. Matching similar gene sequences from various sources can help identify common ancestry among living organisms, including grapes. While there is plenty of documentation and research on the DNA fingerprint analysis on the history of various wine types and vintages, the source of the DNA from these studies is always from the grapes or grape vines themselves, not from actual finished wine samples. The DNA must be extracted from the pulpy mass of the plant, often from the leaves or the root stems. The actual wine itself is essentially pure liquid with no pulpy mass included. And DNA present in the actual wine has been sitting in solvent (water and ethanol) for extended periods of time and is likely highly degraded. Extracting a useful DNA sample from wine itself would likely be impossible.
But that doesn't mean that you are out of options. There are plenty of other ways to quantitatively and qualitatively analyze and characterize wine besides DNA analysis. Color, acidity, and the presence of various chemicals like tannins or inorganic salts derived from the water (like sodium or magnesium) can all be studied and compared to see if your wines match. Be prepared, though, because while such lab analysis is available to anyone by contract companies, the work itself will not be inexpensive so you will have to judge how much this really means to you.