The story
Wrong first meant something physical: crooked, twisted, uneven. Late Old English wrang was shaped by Old Norse rangr / vrangr, "crooked, wrong", and the family goes back to a Germanic root for twisting — the same idea behind wring. Something "wrong" was literally bent out of true; the moral sense ("not right") grew from the physical one, just as right first meant "straight".
Like write, the word began with a pronounced W gliding into R. The Norse form had already lost it in some dialects (rangr), but English held on to the W in speech through the Middle Ages and only reduced wr- to plain R around the 1600s.
The spelling had settled by then. So wrong keeps a W that marks its history — and its kinship with wring, wrist and wrinkle, other "twisting" words that kept the same silent W.
