Cod liver oil has certain benefits that can help with acne:
(1) It contains Vitamin D, which helps neutralize free radicals that damage the skin.
(2) It contains large amounts of Vitamin A, which encourages cell renewal. This helps with acne scars as old skin is replaced by newer, healthy skin.
(3) It contains Omega-3 Fatty Acids, which are anti-inflammatory agents.
In an experiment published by US National Library of Medicine, they found fish oil to be associated with an improvement in acne levels: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3543297/