Yes, you can. Serum is a common source of DNA for molecular analysis.
http://www.clinchem.org/content/55/3/587.full
There are some kits to choose (e.g. http://www.lifetechnologies.com/pl/en/home/references/protocols/nucleic-acid-purification-and-analysis/dna-extraction-protocols/dna-extraction-from-serum.html).