Is the word renunciar the same in Brazilian and European Portuguese?

Yes

The word "renunciar" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only differences are phonetic. In Brazil, the pronunciation of vowels is generally more open and the rhythm is more melodic, whereas in Portugal, vowels are often more closed, reduced, or "hidden," and the speech rhythm is more stress-timed. Additionally, the pronunciation of the "r" varies significantly between different regions of Brazil, while in Portugal, it follows a more standard European phonetic pattern.

Brazilian Portuguese Examples

1. Ele decidiu renunciar ao cargo de diretor. (He decided to resign from the position of director.)
2. Não podemos renunciar aos nossos direitos. (We cannot renounce our rights.)
3. Ela renunciou à herança para ajudar a família. (She renounced the inheritance to help the family.)
4. O político renunciou após o escândalo. (The politician resigned after the scandal.)
5. O réu renunciou ao direito de permanecer em silêncio. (The defendant waived the right to remain silent.)

Continental Portuguese Examples

1. Ele decidiu renunciar ao posto de diretor. (He decided to resign from the post of director.)
2. Não podemos renunciar aos nossos direitos. (We cannot renounce our rights.)
3. Ela renunciou à herança para ajudar a família. (She renounced the inheritance to help the family.)
4. O político renunciou após o escândalo. (The politician resigned after the scandal.)
5. O arguido renunciou ao direito de permanecer em silêncio. (The defendant waived the right to remain silent.)