"the art of government," 1640s, from state (n.2) + craft (n.).
Entries linking to statecraft
state n.2
"political organization of a country, supreme civil power, government," c. 1300, from special use of state (n.1); this sense grew out of the meaning "condition of a country" with regard to government, prosperity, etc. (late 13c.), from Latin phrases such as status rei publicæ "condition (or existence) of the republic."
The sense of "a semi-independent political entity under a federal authority, one of the bodies politic which together make up a federal republic" is from 1774. The British North American colonies occasionally were called states as far back as 1630s; the States has been short for "the United States of America" since 1777; also of the Netherlands. State rights in U.S. political sense is attested from 1798; form states rights is first recorded 1858. Church and state have been contrasted from 1580s. State-socialism attested from 1850.
craft n.
Old English cræft (West Saxon, Northumbrian), -creft (Kentish), "power, physical strength, might," from Proto-Germanic *krab-/*kraf- (source also of Old Frisian kreft, Old High German chraft, German Kraft "strength, skill;" Old Norse kraptr "strength, virtue"). The ultimate etymology is uncertain.
Sense expanded in Old English to include "skill, dexterity; art, science, talent" (via a notion of "mental power"), which led by late Old English to the meaning "trade, handicraft, employment requiring special skill or dexterity," also "something built or made." The word still was used for "might, power" in Middle English.
Use for "small boat" is first recorded 1670s, probably from a phrase similar to vessels of small craft and referring either to the trade they did or the seamanship they required, or perhaps it preserves the word in its original sense of "power."