Millimeter-Wave (mmWave) bands, a key part of future 5G networks, represent a potential channel for RF energy harvesting, where the high-gain antenna arrays offer improved end-to-end efficiency compared to sub-6 GHz networks. This paper presents a broadband mmWave rectenna, the first rectenna realized on a flexible textile substrate for wearable applications. The proposed novel antenna's bandwidth extends from 23 to 40 GHz, with a minimum radiation efficiency of 67% up to 30 GHz, over 3 dB improvement compared to a standard patch. A stable gain of more than 8 dB is achieved based on a textile reflector plane. The antenna is directly connected to a textilebased microstrip voltage doubler rectifier utilizing commercial Schottky diodes. The rectifier is matched to the antenna using a tapered line feed for high-impedance matching, achieving broadband high voltage-sensitivity. The rectifier has a peak RF-DC efficiency of 12% and a 9.5 dBm 1 V sensitivity from 23 to 24.25 GHz. The integrated rectenna is demonstrated with more than 1.3-V DC output from 12 dBm of mmWave wireless power across a 28% fractional bandwidth from 20 to 26.5 GHz, a 15% half-power fractional bandwidth, and a peak output of 6.5V from 20 dBm at 24 GHz.