The proclamation of the Sacred Scriptures has been part of the Mass since the earliest times. During the second Vatican Council the pope and bishops discerned that the faithful needed to be better nourished by the Sacred Scriptures during the liturgy. (Sacrosanctum Concilium 51) This led them to commission the Lectionary for Mass, which increased the quantity of biblical readings on Sundays and weekdays, and expanded the Psalmody by means of the Responsorial Psalm. In order to make sure that the faithful always get a generous portion of the Sacred Scriptures, certain laws were put in place. The General Instruction of the Roman Missal (GIRM) paragraph 61, regulates where the text and antiphon of the Psalm are to come from:
The Psalm texts from the Graduale Romanum and Graduale Simplex are not available in English and may not be suitable for every parish. Musical settings of the Responsorial Psalm that use the antiphons and Psalm texts from the Lectionary are always appropriate. In addition to the Psalms from the Lectionary, the Revised Grail Psalms may also be used since they have been approved for use in the liturgy by the United States Conference of Catholic Bishops.
Musical settings that do not use an approved translation of the Psalms or Antiphons may not be used for the Responsorial Psalm. There are many other legitimate sources, some of which have been listed below. The Liturgy Office is always interested to know of other resources.
OCP Respond and Acclaim by Owen Alstott (Psalms and Gospel Acclamations from the Lectionary for Mass)
GIA Lyric Psalter by Tony Alonso and Marty Haugen (Psalms from Revised Grail Psalter, Antiphons from Lectionary for Mass)
St. Noël Chabanel Responsorial Psalms by Corpus Christi Watershed (Psalm and Response from Lectionary for Mass, free resource)
St. Meinrad Modal Psalm Tones (Requires you to point Lectionary Psalm yourself. Useful for Psalms you can’t find music for)