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

Yes

The word "anunciar" is identical in meaning, spelling, and grammar in both Brazilian and European Portuguese. There are no differences in how the word is defined or how it is conjugated. The differences between the two varieties are strictly phonetic, specifically regarding vowel pronunciation and rhythm. Brazilian Portuguese tends to have more open, unstressed vowels and a more musical, syllable-timed rhythm, whereas European Portuguese features significant vowel reduction (making unstressed vowels sound much shorter or almost silent) and a more stress-timed rhythm.

Brazilian Portuguese Usage

1. A empresa vai anunciar o vencedor hoje. (The company will announce the winner today.)
2. Eu estou anunciando meu carro para venda. (I am advertising my car for sale.)
3. Eles anunciaram a chegada do diretor. (They announced the director's arrival.)
4. Você viu o que o site anunciou? (Did you see what the website announced?)
5. O locutor está anunciando a promoção. (The announcer is announcing the promotion.)

European Portuguese Usage

1. A empresa vai anunciar o vencedor hoje. (The company will announce the winner today.)
2. Estou a anunciar o meu carro para venda. (I am advertising my car for sale.)
3. Eles anunciaram a chegada do diretor. (They announced the director's arrival.)
4. Viste o que o site anunciou? (Did you see what the website announced?)
5. O locutor está a anunciar a promoção. (The announcer is announcing the promotion.)