This work presents a complete IoT-enabled pulse oximeter (PO) system, called OxiSense, made using a custom-designed low power application specific integrated circuit (ASIC) for signal conditioning. One of the novel aspects of the developed system is the testability of all the important modules of the ASIC (both analog and digital) using auxiliary circuits implemented in the ASIC. Another novel aspect is a new embedded and efficient signal-processing algorithm robust to minor motion artifacts. This new algorithm has been implemented on a low-power microcontroller (embedded processing mode) and on a PC using Python (remote processing mode). The PO ASIC is fabricated in 180 nm mixed-mode CMOS technology, and it works at 1.8 V supply voltage. The average power consumption of the analog front-end is 176 µW, and that of the digital module controlling the analog front-end is 23 µW. The prototype PO system made using the custom ASIC operates from a 3.7 V lithium-ion battery and consumes about 8 mW of power. The prototype is housed in a 3D printed casing and it connects with a display device via USB or wirelessly to a laptop/smartphone/tablet. Readings on 20 subjects, both in the lab and in the hospital, show less than 2% deviation in the measured level and worst case deviation of 2.7 beats per minute for the measured heart rate, when compared with the commercial POs.