Born in Frederikssund, Drachmann emerged from the AC Horsens academy in 2006, and grew into a key player in midfield for the club, as well as the team captain.

Drachmann came to AC Horsens as an 18-year-old in the summer of 2006, to complete his education, and at the same time develop as a player on the club's reserve team.

[3] Due to injury to teammate and Horsens star player Allan Søgaard, Drachmann grabbed the opportunity to be the starting defensive midfielder for the club during the 2007–08 Superliga season.

During the next nine years, Drachmann made 171 league appearances for the club, in which he scored four goals, and grew into team captain.

In January 2024, Drachmann was moved into a new role as 'assistant transition coach and responsible for individual training at the academy'.