Two innovative research studies are reported in this paper. One is the sorting of semiconducting carbon nanotubes and ink formulation by a novel semiconductor copolymer and second is the development of CMOS inverters using not the p-type and n-type transistors but a printed p-type transistor and a printed ambipolar transistor. A new semiconducting copolymer (named P-DPPb5T) was designed and synthesized with a special nonlinear structure and more condensed conjugation surfaces, which can separate large diameter semiconducting single-walled carbon nanotubes (sc-SWCNTs) from arc discharge SWCNTs according to their chiralities with high selectivity. With the sorted sc-SWCNTs ink, thin film transistors (TFTs) have been fabricated by aerosol jet printing. The TFTs displayed good uniformity, low operating voltage (±2 V) and subthreshold swing (SS) (122–161 mV dec−1), high effective mobility (up to 17.6–37.7 cm2 V−1 s−1) and high on/off ratio (104–107). With the printed TFTs, a CMOS inverter was constructed, which is based on the p-type TFT and ambipolar TFT instead of the conventional p-type and n-type TFTs. Compared with other recently reported inverters fabricated by printing, the printed CMOS inverters demonstrated a better noise margin (74% 1/2 Vdd) and was hysteresis free. The inverter has a voltage gain of up to 16 at an applied voltage of only 1 V and low static power consumption.