It's hard to for me to compare directly because the US standards are expressed as miles/gallon while the EU standards are g CO2/km, but I think the US has about the same standards as the EU, although historically trailing by 5 years or so: http://www.rff.org/files/document/file/RFF-PB-16-03.pdf

But answering the implied general question, yes, the US does have legally mandated efficiency standards for vehicles, and the total number of miles driven is about 3 times what it was in 1970: https://www.afdc.energy.gov/data/10315.