The bill would also create an English language requirement for naturalization into the United States, and require the federal government to encourage people to learn the language.
While the bill is largely backed by Republicans in the House, it does boast a few Democratic cosponsors: Reps. Mike McIntyre (N.C.) and Nick Rahall (W.Va.).
Inhofe said this week that as Congress considers immigration reform, the English-only bill should be part of that discussion.
"Congress will likely be debating comprehensive immigration reform this summer, and any reform to our immigration laws must include English language provisions," he said. "We are a nation built by immigrants, and it is important we share one vision and one official language."
In the last Congress, King's bill ended up with 122 cosponsors. But while it was the subject of a House Judiciary subcommittee hearing, it was not brought to the floor for a vote in the Republican-led House.
The bill is H.R. 997 in the House and S. 464 in the Senate.