"to burn superficially or slightly, but so as to change the color or injure the texture," early 14c., scorchen, perhaps an alteration of scorcnen "make dry, parch; become singed" (late 12c.), itself a word of obscure origin, perhaps from Old Norse skorpna "to be shriveled," which is cognate with Old English scrimman "to shrink, dry up."
The old derivation is from Old French escorchier "to strip off the skin," from Vulgar Latin *excorticare "to flay," from ex- (see ex-) + Latin cortex (genitive corticis) "cork;" but OED and Century Dictionary find this not likely based on the sense difference. That word came into English separately as scorchen "strip the skin from" (mid-15c.).
Scorched earth military strategy is by 1937, said to be a translation of Chinese jiaotu, in reference to tactics to stem the Japanese advance into China. The tactics themselves are much older.