It's OK, but it's a little old-fashioned and not what most native speakers would say these days.
In modern English, it's more common to say either "I don't have any brothers or sisters" or "I haven't got any brothers or sisters".
Using 'have' in its auxiliary form with this meaning without 'got' is increasingly rare. For example, nobody has said "I haven't a car" in standard English for a long time. However, we sometimes still use the auxiliary form of 'have' without 'got' when the object includes such words as any/no/ much/many - as in "We haven't much time" and in deliberately old-fashioned phrasings such as "Have you no shame?".
Otherwise, we always say either 'don't have x' or 'haven't got x'. 'Haven't got' is slightly more informal and more common in BrE than in AmE.