Paragraph 937 of the Catechism is part of an "In Brief" section that occurs at the end of every topic of the Catechism. The "In Brief" sections are intended to summarize the paragraphs that have gone before. In this case, the paragraph is restating material that occurs in paragraphs 881 and 882. In particular:
"For the Roman Pontiff, by reason of his office as Vicar of Christ, and as pastor of the entire Church has full, supreme, and universal power over the whole Church."
paragraph 881
This is a quote from the Vatican II document Lumen Gentium. The Scriptural references supporting the statement are John 21:15-17 (" Feed my sheep") and Matthew 16:18-19.
Similarly, the constitution Pastor aeternus, promulgated by the First Vatican Council, states in Chapter III:
Full power was given to [the Roman Pontiff], in Blessed Peter, by Jesus Christ our Lord, to pasture, to rule, and to govern the Universal Church...
The specific quote that appears in paragraph 937 itself is found in the preface to the decree Christus Dominus, promulgated by Pope Paul VI in 1965.
