David Hall says he does not mind if he loses his job after refusing on several occasions to watch the 17-minute video.
He has worked in information technology for 14 years at the agency's office in Illinois.
Speaking to the News-Gazette, he said he was asked to watch the video, which promotes respect and inclusion, in April 2016.
Hall, 42, said he is a Christian and does not think God would have wanted him to see the video, telling the paper signing the form saying he had watched it would be to "certify sin."
On two previous occasions when he refused to watch the video, he was suspended without pay.
He said he does not see why he should watch it as he does not have a public-facing job and says he has a right to freedom of religion.
Social Security Administration released a statement saying: "In support of an inclusive work environment, as well as exemplary customer service, the Social Security Administration recently announced a diversity and inclusion training on the Lesbian, Gay, Bisexual and Transgender (LGBT) Community to our employees.
"The training includes a brief session on tips for increasing cultural awareness in a diverse and inclusive environment."
Hall says he expects to lose his job: "This is something I want to fight and expose, to give other Christians the courage of their convictions."
He added that he had hired representation if the case goes further.
