Android operating system restricts access to data by enabling data control flow and permission systems to reduce the risk of information theft. Therefore, attackers are constantly looking for alternative and stealthy approaches to exfiltrate private data from a targeted device. This paper presents CovertPower, a covert channel attack that exfiltrates user data by actively inducing power consumption on Android devices. At the transmitting end, our CovertPower app modulates binary data into a timed resource workload (e.g., processor, write-on-memory), producing power consumption bursts. On the receiving end, we acquire power consumption traces via a low-cost hardware tool that can be easily concealed in USB wall-socket adapters or powerbanks. Therefore, a signal processing-based decoder analyzes such traces and retrieves the exfiltrated information. We demonstrate the feasibility of our attack with a thorough experimental evaluation on 14 mobile devices and various real-world settings such as display state, ongoing activities, and charging technologies. Our attack achieves a transfer speed of up to 10bps with a high bit sequence similarity on most devices and settings considered.