Yes. You could do this by adding solvents to break down any cell walls, centrifuge to separate the DNA, if you haven't got much then upscale with PCR, gel electrophoresis could be used to detect the DNA, and Sanger sequencing to find the sequence.
RNA has great capability as a genetic molecule; it once had to carry on hereditary processes on its own. It now seems certain that RNA was the first molecule of heredity, so it evolved all the essential methods for storing and expressing genetic information before DNA came onto the scene.
I agreed with him for 100%