Yes, alcohol consumption can indeed increase the risk of cancer. The more alcohol people drink, the greater their increase of cancer, particularly breast cancer. This is due to alcohol's effects on cells, which include changes in gene expression. Cancer, or the growth of tumors, is a dysregulation in cell cycles. Alcohol can increase tumor growth and decrease the molecules that suppress and combat tumor growth.
There's a 4 to 13% increase in the risk of cancer, particularly breast cancer, for every 10 grams of alcohol consumed daily. This is equivalent to one drink per day in the US. However, it's important to note that consuming folate and B12 might partially offset some of this increased risk, but it's not a guarantee.