Yes, of course.
It is narrated that the Prophet (S) said, "Nothing wards off fate except supplication."
It is narrated that Imam al-Kazim (A) said, "I urge you to supplicate, for verily supplication to Allah and seeking from Allah repels calamity which may have been destined and decreed with just the execution remaining, so if Allah is supplicated and is asked to avert a calamity, it is averted."
The Qur'an also strongly encourages us to call to God and seek what we want or need from Him.
Also, certain acts, such as giving charity, can change aspects of our fate that have been decreed.
Of course, sometimes Allah does not grant our requests, out of His wisdom or as part of a greater plan.
There are some things in our fate that are fixed and unchangeable, and some things that are changeable; we don't know which are which, so we can do du'a regarding all of them, and leave the response to Allah.