Build in a highball glass over ice.
According to David Herpin
This drink is widely believed to be created in the 1950's by a type of worker who carries a screwdriver in their toolbelt. It is said that these workers first mixed vodka and orange juice with a "screwdriver". Let's look at the facts, here is an early printing of this drink:
Journalism quarterly: Volume 44 in 1938 "And answered it "The famous Smirnoff Screwdriver", Just pour a jigger of smirnoff vodka over ice cubes, fill glass with orange juice and serve"
Then later it is published that this drink was invented by american aviators in:
Newsweek: Volume 23 in 1944 "A Screwdriver —a half-orange-juice and half-vodka drink popularized by interned American aviators—costs a dollar including the customary barman's tip."
This "American Oil Riggers" could come from these stories printed in:
Time: Volume 54 by Briton Hadden, Henry Robinson Luce in 1949 "In the dimly lighted bar of the sleek Park Hotel, Turkish intelligence agents mingle with American engineers and Balkan refugees, drinking the latest Yankee concoction of vodka and orange juice, called a "screwdriver"."
Lands east: the Near and Middle East magazine: Volumes 1 - 2 by Near East Society, Middle East Institute (Washington, D.C.), Near East College Association in 1948 "For cocktails or after dinner consumption, some travelers enjoy the "screwdriver" (reputedly a GI concoction from the Persian Gulf Command days made of equal parts of vodka and orange juice)."
Smirnoff Vodka did run an advertising campaign for the "smirnoff screwdriver" from 1937 - 1961 and appears in hundreds of magazines, here are a few:
LIFE - Oct 17, 1955 - Page 153 Vol. 39, No. 16; LIFE - May 26, 1958 - Page 107 Vol. 44, No. 21; LIFE - Jun 15, 1959 - Page 63 Vol. 46, No. 24; Ebony - Oct 1960 - Page 67 Vol. 15, No. 12; LIFE - May 26, 1961 - Page 113 Vol. 50, No. 21
This drink dates between 1936-1938 and was very likely the creation of the "Smirnoff Vodka" marketing team. It contained at least as of then.
Shake these ingredients:
Strain over fresh ice cubes in a glass (undetermined
"Time Magazine," 24th October 1949
In the dimly lighted bar of the sleek Park Hotel, Turkish intelligence agents mingle with American engineers and Balkan refugees, drinking the latest Yankee concoction of vodka and orange juice, called a "screwdriver."
"TIMES-RECORDER," Zanesville, Ohio, 24th December 1952
"BRING ME a screwdriver, please," a customer told a waiter in a cafe here the other day. "A screwdriver? Is there something wrong with the table, sir?" said the waiter...who found out, that way, that a "screwdriver" is a mixture of vodka and orange juice.
"After You, Marco Polo," by Jean Bowie Shor, 1955
"Slender girls and lithe young men filled the bar where we repaired each evening for a screwdriver — a noxious combination of orange juice and vodka which was born in Ankara and has since migrated to America."
HOUSE & GARDEN, "Cocktail lore and legend," April 1965
"The Bloody Mary, favorite morning-after restorative, is claimed by George Jessel and at least two New York bartenders, while the screwdriver, which tastes like orange juice but is considerably more potent, is believed to have originated with American oil workers in Iran who drank vodka and orange juice, stirring it with screwdrivers they carried attached to their fatigue pants by loops."