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There is no doubt: Yes, baptism by immersion is permissible.
The Congregation for the Doctrine of the Faith has stated, while considering the validity of Mormon baptism:
I. The Matter. On this point there is no problem. Water is used. The Mormons practice Baptism by immersion (cf. Doctrine and Covenants [D&C] 20:74), which is one of the ways of celebrating Baptism (application of the matter) which is accepted by the Catholic Church.
The CDF actually rejected the validity of Mormon baptism, but using immersion was not one of the reasons for the rejection.
It also features in the Catechism:
1239: Baptism is performed in the most expressive way by triple immersion in the baptismal water. However, from ancient times it has also been able to be conferred by pouring the water three times over the candidate's head.