I don't know what his connection is to the rest of the Badgers but here is more information that is probably the same person:

5/9/1733 Book BB p296: "John Andrew, Sr., planter of Colleton Co.(SC), to his loving & obedient son, John Andrew, Jr., for love and affection 150 a., English measure, in St. Bartholomew Parish, bounding E. on John Hains; S on George Badger & John Mitchell; W. on George Mitchell, Sr., N on the plantation on which John Andrews Sr. lives. Witnesses: Joseph Andrews, Joseph Mitchell. Before Culcheth Golightly, J.P. James Homes, Pub. Reg."
From South Carolina Deed Abstracts 1719-1772 Vol. II by Clara A. Langley, 1984.

8/16-17/1738 Deed Book T, p181: "Hugh Campbell, planter, and Ann his wife to James Kirving, surgeon, all of Colleton Co. for L574 SC money, 164a. in Colleton Co., (136a. of which had been purchased on 2 Sept 1726 from Alexander Trench by George Badger, and sold by Badger to Campbell on 12 Jan. 1730; the other 28a. being part of 31a. granted to Campbell by Col. Broughton on 25 June 1736); bounding S on Lawrence Woolfordson and Jospeh Barker; E on Isaac Haynes; N on Isaac Haynes & John Andrews; W on Christopher Smith. Witnesses: John Andrews, Alexander Sproull. Before James Bullock, J. P. Robert Austin, Pub. Reg." From South Carolina Deed Abstracts 1719-1772 Vol. I, by Clara A. Langley, 1983.