High precision and large dynamic range measurement are required in the readout systems for the Water Cherenkov Detector Array (WCDA) in Large High Altitude Air Shower Observatory (LHAASO). This paper presents a prototype of 12-bit 40 MSPS Analog-to-Digital Converter (ADC) Application Specific Integrated Circuit (ASIC) designed for the readout of LHAASO WCDA. Combining this ADC and the front-end ASIC finished in our previous work, high precision charge measurement can be achieved based on the digital peak detection method. This ADC is implemented based on power-efficient Successive Approximation Register (SAR) architecture, which incorporates the key parts such as Capacitive Digital-to-Analog Converter (CDAC), dynamic comparator and asynchronous SAR control logic. The simulation results indicate that the Effective Number Of Bits (ENOB) with a sampling rate of 40 MSPS is better than 10 bits in an input frequency range below 20 MHz, while its core power consumption is 6.6 mW per channel. The above results are good enough for the readout requirements of the WCDA.