Not sure if this is what you're looking for... but the Treasury of Scripture Knowledge has the following entries for
James 1:12:
James 1:12
the man:
James 1:2-4,
James 5:11;
Job 5:17;
Psalm 94:12,
Psalm 119:67,
Psalm 119:71,
Psalm 119:75;
Proverbs 3:11-12;
Hebrews 6:15;
Hebrews 10:32,
Hebrews 12:5;
Revelation 3:19
when:
Deuteronomy 8:2,
Deuteronomy 13:3;
Proverbs 17:3;
Zechariah 13:9;
Malachi 3:2-3;
Hebrews 11:17;
1 Peter 1:6-7;
1 Peter 5:10
the crown:
Matthew 25:34;
Luke 22:28-30;
Romans 2:7-10;
1 Corinthians 9:25;
2 Timothy 4:8;
1 Peter 1:7, 1 Peter 4:13;
1 Peter 5:4;
Revelation 2:10,
Revelation 3:21
which:
James 2:5;
Isaiah 64:4;
Matthew 10:22,
Matthew 19:28-29
them:
James 2:5;
Exodus 20:6;
Deuteronomy 7:9;
Nehemiah 1:5;
Psalm 5:11;
Romans 8:28;
1 Corinthians 2:9, 1 Corinthians 8:3;
1 Peter 1:8;
1 John 4:19.
The passages listed under "them" (underlined above) appear to be what you were looking for - a passage dealing with the "promise that was made to those that love Him" that James was referring to, though they are not in the book of James itself.
It may be that the phrase was in such usage at the time that James' audience would have grasped it immediately and attached the saying to one of the several similar promises they had heard read from the only Bibles they had - The Hebrew Scriptures (our "Old Testament").