Romans 6:1-10: "1 What shall we say then? Are we to continue in sin that grace may abound? 2 By no means! How can we who died to sin still live in it? 3 Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? 4 We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life.
"5 For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. 6 We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. 7 For one who has died has been set free from sin. 8 Now if we have died with Christ, we believe that we will also live with him. 9 We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. 10 For the death he died he died to sin, once for all, but the life he lives he lives to God."
Ephesians 5:25b-26: "as Christ loved the church and gave himself up for her, 26 that he might sanctify her, having cleansed her by the washing of water with the word"
Ezekiel 36:25-27: "25 I will sprinkle clean water on you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you. 26 And I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh. 27 And I will put my Spirit within you, and cause you to walk in my statutes and be careful to obey my rules.
Galatians 3:26-27: "26 for in Christ Jesus you are all sons of God, through faith. 27 For as many of you as were baptized into Christ have put on Christ."
+++
The lines "Consider now what God has done / The gifts He gives to ev'ryone / Baptized into Christ Jesus!" in the hymn's first verse seem to refer to the text from Romans 6.
The third verse incorporates the texts from Ephesians 5 and Ezekiel 36.
Galatians 3:26-27 appears at the beginning of the fourth verse: "In Baptism we now put on Christ."
The beginning of the sixth verse ("So use it well! You are made new - / In Christ a new creation!") comes from 2 Corinthians 5:17: "Therefore, if anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come."