Not according to the EIA.
The small print/footnote:
Notes: Crude oil exports are restricted to: (1) crude oil derived from fields under the State waters of Alaska's Cook Inlet; (2) Alaskan North Slope crude oil; (3) certain domestically produced crude oil destined for Canada; (4) shipments to U.S. territories; and (5) California crude oil to Pacific Rim countries.Enough exceptions to drive a semi truck through loaded with crude oil.
By the way, "California crude oil to Pacific Rim countries." Can that dot be connected to the fact that OXY USA (big in California) plans to re-deploy some of its rigs to California and out of North Dakota? WTI and North Dakota Light Sweet significantly less than Brent oil? Hmmmm?
By the way, for Bakken and Spearfish fans, you have to love the phrase "certain domestically produced crude oil destined for Canada."