
Does this mean that the twins are sons or daughters of the speaker?

Yes, indeed.

How would you translate this then?
I have a twin.
http://tatoeba.org/eng/sentences/show/2252512
I'm not sure if the English is correct. I want to mean "I have a twin brother or a twin sister."

Ah, good question!
While "Ich habe Zwillinge." (plural) can only mean that you have twin children, because they're two, "Ich habe einen Zwilling." means that you have a twin brother or sister (sex is undefined here).
As far as I know, the English should be correct. I'm not a native speaker of English though, but I guess it's similar there:
"I have a twin." = I have a twin brother or a twin sister.
"I have twins." = I have two identical sons or daughters.

Interesting enough! Thank you for the explanation.

An Tommy:
Hier hast Du eine Herausforderung zum Übersetzen: http://tatoeba.org/deu/sentences/show/2252811. Es handelt sich um einen Literaturbeleg des Wortes „Zwillingsgeschwister“. ☺

なんかめっちゃガチなのがきたーヾ(・ω・`;)ノ
ちょっとゆっくり取り組みますね。
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This sentence was initially added as a translation of sentence #2252516
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