Sim, você pode, mas potencialmente, renunciar a outras cidadanias:
"Os cidadãos não-europeus e não-suíços devem geralmente renunciar à sua antiga cidadania se quiserem se tornar cidadãos alemães."
Além disso, dependendo de quando você nasceu, pode ser bastante complicado. Veja este artigo da Wikipédia para os detalhes sobre Lei de nacionalidade alemã :
Descent from a German parent
A person born of a parent with German citizenship at the time of the child's birth is a German citizen. Place of birth is not a factor in citizenship determination based on parentage.
- Those born after 1 January 1975 are Germans if the mother or father is a German citizen.
- Those born before 1 January 1975 could normally only claim German citizenship from the father and not the mother. Exceptions included cases where the parents were unmarried (in which case German mothers could pass on citizenship) or where the German mother applied for the child to be registered as German on or before 31 December 1977.
- Special rules exist for those born before 1 July 1993 if only the father is German and is not married to the mother. The father must acknowledge paternity and must have married the mother before 1 July 1998.
- A child born in a foreign country will no longer receive German citizenship automatically by birth, if his/her German parent was born after 31 December 1999 in a foreign country and has his/her primary residence there. Exceptions are: The child would be stateless. The German parent registers the child's birth within one year of birth to the responsible German agency abroad.
- In case both parents are German citizens, German citizenship will not be passed on automatically, if both parents were born abroad after 31 December 1999 and have their primary residence outside of Germany. Exceptions are same as the above.
- Those born in Germany and adopted to a foreign country would need to contact their local German Consulate for clarification of German citizenship. Persons who are Germans on the basis of descent from a German parent do not have to apply to retain German citizenship by age 23. If they acquire another citizenship at birth, they can usually continue to hold this.