The emperors have often spoken many languages and Hungarian was an important one so one may find numerous Habsburg rulers who spoke Hungarian, too.
For example, Maximillian II fluently spoke Spanish, French, Latin, Hungarian, and Italian. Maria Theresa spoke German, Italian, French, Spanish, Latin, Czech and she added Hungarian before she became the empress.
The long-time "last" emperor Franz Joseph I of Austria was led to his skills by his mother Sophia and he was proud about them. He could speak, write, and read in French, Italian, Hungarian, and Czech. His successor Charles I of Austria did speak Czech extremely well (and he wanted some autonomy for the Czech lands around the time of the First World War) but I am not able to find out whether he spoke Hungarian.
However, Charles' recently deceased son Otto von Habsburg (1912-2011) surely did. If we count German, he spoke 15 different languages that included Hungarian and Czech. He has also passed the standard Austrian as well as Hungarian high school (gymnasium) requirements. Nevertheless, even with these credentials, he wasn't allowed to restore the Habsburg monarchy.
Almost all the members of the Habsburg House in the 20th century spoke Hungarian.