German does not have a single word for this - and in fact, this isn't as easy to express as in english.
In german, when you say
Das ist mein(e) Freund(in)
most people will assume its your boyfriend/girlfriend.
However, if you say
Das ist ein(e) Freund(in) (von mir)
then most people will understand its just a friend, not your boyfriend/girlfriend.
So the difference is in mein(e)/ein(e), which makes it a bit hard to grasp.
With same-sex relationships, its not that easy. Most people will simply not assume you are gay/lesbian, unless you came out to them before.
You can, however, use other terms to refer to your boyfriend/gilfriend.
While young people (teens mostly) will prefer "Freund(in)", adults often use Partner(in) or Lebensgefährt(e/in) to describe their romantic partner.
This works very well for same-sex partnerships, too, and is in fact what I'd recommend using.
If a male person introduces someone as his "Lebengefährte", its quite damn clear what he meant. No confusions. Same applies for female and "Lebensgefährtin".
Its also clear if you talk about other persons. If you have a gay friend and talk about his "Lebensgefährte", everyone will understand. If you talk about his "Freund", not so much.