Is it possible to get the huntington gene even though there's no family history of the disease?

Yes. Huntington disease is autosomal dominant, meaning that affected individuals have one normal and one abnormal gene. Offspring of an affected parent (like arlo guthrie) have a 50% chance to get the abnormal gene. The expanded trinucleotide repeat that constitutes the abnormal gene can develop as a new mutation without prior cases in the family.