The RF pulse generator in nuclear magnetic resonance (NMR) systems plays a crucial role in determining imaging quality. Traditional direct digital synthesis (DDS) techniques rely on large-capacity lookup tables to achieve high precision, which results in excessive consumption of on-chip block random access memory (BRAM) resources and limits flexibility. This paper proposes a design for a magnetic resonance radiofrequency pulse generator based on the coordinate rotation digital computer (CORDIC) algorithm. By implementing a custom CORDIC core within a field-programmable gate array (FPGA), it achieves digital modulation of the radiofrequency signal's frequency, phase and amplitude. Combined with a Zynq-7000 system-on-chip (SoC), this design provides a highly integrated and low-power hardware architecture. Experimental results demonstrate that the proposed pulse generator can output RF pulses with a frequency resolution of 0.046 Hz and a phase resolution of 0.005 5˚, Moreover, the BRAM resources occupied by the four channels are reduced by approximately 21.4% compared to the traditional DDS solution. This design offers a feasible solution for achieving miniaturization and high performance in the RF front-end of NMR instruments.