Randolph's parents were John Wrenn who died in 1722 and Ann (Smith) Carrell who died prior to Jan. 1767, which was shortly after Randolph's birth.
The death of John & Ann left Randolph and his three siblings orphans. All four of these children were:
John Wrenn m. Polly Lawrence in 1782,
Robert Wrenn m. Hannah Davis in 1783.
Sarah "Sally" Wrenn m. Thomas Newsum on 8/16/1786.
Randolph Wrenn m. Martha Jones in 1789
Sources
Dorothy F. Napoli, "Randolph Wren in Virginia – his parents, siblings, and extended family: correcting the record." Annals of Genealogical Research Vol. 10, No. 1 (2014) at http://www.genlit.org/agr/viewarticle.php?id=58
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DNA Connections
It may be possible to confirm family relationships with Randolph by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Randolph: