Acne can definitely run in the family - if your parents had acne than you are likely to get it as well particularly if both of your parents suffered from the condition. There is no one acne ‘gene’, however a study of identical twins found that approximately 81% of the tendency to developing acne is caused by genetic (inherited) factors [Journal of Investigative Dermatology 119: 1317].
A genetic study of 3823 patients aimed to discover genes that explain this propensity for acne to run in the family. They identified links with 15 genomic locations. Whilst the full details by which all of these genes influence acne development are not completely understood, interestingly many are regulators of cell behaviour in the skin and hair follicle [Nature Communications 9:5075].