On-chip copper (Cu) based self-rolled-up membrane (S-RuM) inductors are demonstrated for the first time. Compared to the gold (Au) based S-RuM inductor, device structures and fabrication processes are re-designed to realize CMOS compatibility by switching conduction metal to Cu and overcoming related processing challenges. Performance enhancements include ∼44% reduction of conduction layer resistivity compared to Au-based with the same thickness, and a clear path to 100% fabrication yield are achieved. RF measurement shows as high as ∼ 61nH/mm2 inductance density with just a 2-turn structure for these air-core S-RuM inductors. The achieved inductance is in the range from 0.3nH to 1nH. The best self-resonant-frequency (SRF) and quality factor (Q factor) of 1nH device is ∼23GHz and ∼2.4@5GHz, respectively. Much better performance can be readily obtained by rolling up more turns and integrating soft magnetic material thin film and core. Results show that Cu S-RuM inductor is very promising to replace on-chip planar inductor with better performance as a new industry standard.