Is there a sin on someone who studies English as an external student at university, even though their primary intention is to achieve worldly goals such as a career promotion, with a subsequent intention to use it for calling people to Allah?

Learning the English language is permissible (mubah), and it may become a communal obligation (fard kifayah) if there is a need for it for the benefit of Muslims. The questioner is allowed to learn it and pursue his university studies in it for worldly benefits, provided that he has acquired the necessary amount of Islamic knowledge. However, it is better to utilize one's time in seeking sacred knowledge (al-ilm ash-shar'i) due to the scarcity of those pursuing it and the people's need for it, or in performing good deeds that will benefit one in the hereafter, such as prayer, reciting the Quran, and serving Muslims. This is especially true since this worldly life is fleeting, and one should hasten towards the hereafter. This is further emphasized for those who have reached the age of forty.