The video consisted of dashcam footage and was shared on YouTube and across social media, amassing 2,000 views.
It showed a white dog being carried by what appeared to be its neck on Hill Street, Hednesford on June 12.
The publisher of the video shared it in hopes of finding out why the dog was being carried in that way, due to concerns for its safety.
Now, the man has handed himself into police and a referral has been made to the RSPCA – the video has now been removed offline.
A spokesperson for Staffordshire Police said: "Police were notified of a video circulating on social media on Sunday whereby a man with a dog was recorded in Hednesford.
"The man has come forward to officers and a referral has been made to the RSPCA."