Strictly speaking, No. In the loosest sense, maybe.
It depends on what you mean “Cast out demons”. Casting out demons means exorcism, and this is reserved only to an ordained priest. There are two kinds of exorcisms:
The one a priest carries out during the baptism of a catechumen or an infant. The Rite of Baptism in the Extraordinary Form of the Roman Rite has the following prayer:
I cast you out, unclean spirit, in the name of the Father, + and of the Son, + and of the Holy + Spirit. Depart and stay far away from this servant of God, N., For it is the Lord Himself who commands you, accursed and doomed spirit, He who walked on the sea and reached out His hand to Peter as he was sinking. So then, foul fiend, recall the curse that decided your fate once for all. Indeed, pay homage to the living and true God, pay homage to Jesus Christ, His Son, and to the Holy Spirit. Keep far from this servant of God, N., for Jesus Christ, our Lord and God, has freely called him to His holy grace and blessed way and to the waters of baptism.
I am almost certain you may have seen a movie, a picture or heard a story about a demoniac being exorcised. This is usually colorful and dramatic. Whilst such movies might exaggerate things or even depart entirely from reality, sometimes they could actually be close to what a priest who performs a solemn exorcism experiences. Exorcisms are very very dangerous and when could actually go wrong, so it is not something to be taken lightly.
Only a priest, with special training and express authority from his local bishop can perform a solemn exorcism. Solemn exorcisms are very rare and is a very long process. Some cases take month to a year. And there must be exhaustive medical evaluations to make sure there’s no chance the suspected demoniac isn’t actually suffering some medical problems. There have been cases where people with mental illnesses have been branded “possessed” and this has caused many people pain, suffering and even death. This is why the rule on exorcism is so strict that many dioceses in the world don’t even perform any in years.
“When the Church asks publicly and authoritatively in the name of Jesus Christ that a person or object be protected against the power of the Evil One and withdrawn from his dominion, it is called exorcism. Jesus performed exorcisms and from him the Church has received the power and office of exorcizing. In a simple form, exorcism is performed at the celebration of Baptism. the solemn exorcism, called “a major exorcism,” can be performed only by a priest and with the permission of the bishop. the priest must proceed with prudence, strictly observing the rules established by the Church. Exorcism is directed at the expulsion of demons or to the liberation from demonic possession through the spiritual authority which Jesus entrusted to his Church. Illness, especially psychological illness, is a very different matter; treating this is the concern of medical science. Therefore, before an exorcism is performed, it is important to ascertain that one is dealing with the presence of the Evil One, and not an illness.”
“In 1999, the Catholic Church carried out its first major update to the rules surrounding exorcism since 1614 and distinguished between demonic possession and physical or psychological illness.
As a result, Father Thomas (an exorcist) works with a team of doctors, psychologists and psychiatrists – all practising Catholics – to rule out any other cause for a person’s suffering before diagnosing demonic possession.” BBC
No, you do not have the power to cast out demons if you’re talking about the above. However, you could cast out demons by praying to God for protection from their influence, or by saying simple prayers asking God to free your home from the onslaught of evil. In this loose sense, yes, any Catholic can “cast out demons”. But not in a solemn or strict sense. Only an ordained priest has the faculties to conduct the rite of exorcism.