Is it possible to trace of the ancestry of a person by only using his/her genetic information?
In short, yes, it is possible. There are companies that sequence part of your genome and then can trace it back to your ancestors. All human family trees can be traced back to their African origin 200 000 years ago, but the companies that sequence your genes do not do that. For example, 23andMe sequences only 1 million of your base pairs (single nucleotide polymorphisms (SNPs)). They trace your most recent heritage, which could lead to Europe, Africa, or Asia. They can basically trace which part of your chromosomes (and thus your ancestry) came from your mom or your dad:


  Unlike the sex chromosomes and the mitochondrial DNA, which are inherited as blocks, the 22 biparental chromosomes, known as autosomes, are scrambled during reproduction. Through a process known as recombination, each parent pulls his or her paired set of 22 autosomes into chunks, then reassembles a new single set using half the material from each pair. The two single sets of chromomes from each parent are combined into a new paired set when a sperm fertilizes an egg. 


You can read more about 23andMe here. There are other companies that are specialized in tracing your ancestry: Genetic Genealogy, DNA Tribes, and Heirlines.