Moore County was formed in 1784 from Cumberland County.
This county has seen many border changes over the years that researchers should be aware. See The Formation of the North Carolina Counties, 1663-1943, by David Leroy Corbitt for a complete history of the county formation. (Affiliate Link)
U.S. Enumeration Maps 1900-1940 for this county can be found on FamilySearch in the unindexed files. Here is a direct link to this North Carolina county’s Enumeration Maps.
There are several maps, make sure to scroll forward and backward from this starting link. For more information about these maps go here.
You will need a free account at FamilySearch.org to access these images. If you already have an account, this link should direct you to login first.