Probably not precisely. Chromosomal DNA is a very long molecule that is constantly undergoing mutations. However, the ends of chromosomes, the so-called telomeres do get shorter over time. So, theoretically you could tell by looking at telomere length (at best a rough estimate), but since everyone starts with a unique length to begin their life, there is no way to determine a precise age with a “snapshot” how much shorter the telomere is relative to the initial one.
In theory (but not in practice), if you had DNA from birth, and then collected DNA at intervals over a lifetime, you might be able to predict age (relatively speaking), but the shortening of the telomeres is also not a finite or predictable event, and as such you would only be able to generate a very rough estimate. This would also depend on the which cell type you used to measure the telomeres, as this too varies within an individual.