Psalm 37:5: "Commit your way to the LORD; trust in him, and he will act."
Psalm 125:1: "Those who trust in the LORD are like Mount Zion, which cannot be moved, but abides forever."
Philippians 4:6-7: "6 do not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God. 7 And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus."
1 Peter 5:6-7: "6 Humble yourselves, therefore, under the mighty hand of God so that at the proper time he may exalt you, 7 casting all your anxieties on him, because he cares for you."
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The two verses from the Psalms and the verses from 1 Peter 5 all appear in the first few lines of the hymn: "Entrust your days and burdens / To God's most loving hand; / He cares for you while ruling / The sky, the sea, the land." The rest of the hymn expands upon this.
The text from Philippians 4 is referred to in the second verse: "No anxious thought, no worry, / No self-tormenting care / Can win your Father's favor; / His heart is moved by prayer."
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The lines "For He who guides the tempests... Will find for you a pathway / And guide you all your days" at the end of the first verse may be drawn from Proverbs 3:5-6: "5 Trust in the LORD with all your heart, and do not lean on your own understanding. 6 In all your ways acknowledge him, and he will make straight your paths."
The lines "Take heart, have hope, my spirit, / And do not be dismayed; / God helps in ev'ry trial / And makes you unafraid" at the beginning of the third verse bear some resemblance to Isaiah 41:10: "fear not, for I am with you; be not dismayed, for I am your God; I will strengthen you, I will help you, I will uphold you with my righteous right hand."
The line "When you with life are crowned" in the fifth verse could refer to either James 1:12 or Revelation 2:10.