I got a job offer from a German company who are ready to sponsor my blue card/work permit for Germany. I am gay and I want to take my partner (husband) with me. We got married in Denmark which allows foreigners to get married. Same-sex marriage is not allowed in my country (not in the EU). Is there a chance that I can take my partner (husband) with me to Germany?
A blue card allows for your spouse and relatives to accompany you.
A "spouse" always means "spouse or registered partner", which is Germany's way of saying "It's a same sex marriage, but it doesn't have 100% the same rights as a married couple, so we don't call it marriage". Registered Partnership has existed for a while. Same sex marriage actually called a marriage and being 100% equal is a relatively new thing just passing parliament this year. Same sex marriages of other states are recognized.
The marriage must have legal validity in Germany. Marriages by tribal law or other marriages with non-state recognition cannot be recognized. In the case of immigration of a partner of the same sex, this must be a „registered partnership“ in the sense of the German Civil Partnership Act or a partnership that is state-recognized according to foreign law.
I cannot think of anything better suited to that "state-recognized" partnership, than an actual marriage in another EU country. So you are good. Just approach whatever government authority issued you that blue card and ask them what form to fill for your husband to join you.