For by one Spirit we were all baptized into one body—whether Jews or Greeks, whether slaves or free—and have all been made to drink into one Spirit. (1 Corinthians 12:13)
There is no mention here of water. Baptism by the Holy Spirit into water is a given.
There is also an antitype which now saves us, baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ.
(1 Peter 3:21)
1 Corinthians 12:13 For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
When one trusts the Lord after hearing and believing the word of truth (1 Corinthians 15:1-4) they are baptized by one Spirit in to one Body (1 Corinthians 12:13).
It is a baptism (identification) into Christ's death,
Romans 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? 4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. 5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
It's a Spirit baptism into Christ,
Galatians 3:27 For as many of you as have been baptized into Christ have put on Christ.
It is the one baptism of Ephesians 4 that we are to endevour to keep.
Ephesians 4:1 I therefore, the prisoner of the Lord, beseech you that ye walk worthy of the vocation wherewith ye are called, 2 With all lowliness and meekness, with longsuffering, forbearing one another in love; 3 Endeavouring to keep the unity of the Spirit in the bond of peace. 4 There is one body, and one Spirit, even as ye are called in one hope of your calling; 5 One Lord, one faith, one baptism, 6 One God and Father of all, who is above all, and through all, and in you all.
It has NOTHING to do with water! The Spirit is the baptizer!