Green’s Dictionary of Slang

zig n.²

In phrases

get the zig (v.) [? fig. use of zig-zig n., i.e. ‘fucked (off)’]

to become angry.

2000		J.J. Connolly Layer Cake 18: Some sloppy little teams got the zig cos we wouldn’t trade with them.
2011		J.J. Connolly Viva La Madness 101: ‘Know fuckin what, Sonny?’ I’m getting the zig now.