This work presents the design of a low power 24 GHz LC cross-coupled voltage-controlled oscillator (VCO) for a frequency modulated continuous wave (FMCW) radar base station. The VCO is fabricated using 45 nm RF -SOI technology since its passive components provide better quality factor than those of bulk CMOS technologies. When measured on a printed circuit board (PCB), the fabricated VCO consumes only 12.3 mA from a 1 V supply, achieving a power efficiency of 2.15 GHz/mW which outperforms other state-of-the-art LC cross-coupled VCOs. The design employs a two bit capacitor bank to achieve a tuning range of 9%. The measured phase noise is -96.4 and -119 dBc/Hz at 1 and 10 MHz offset frequency respectively. It achieves a figure of merit (FOM) of -179.5 dBc/Hz at 10 MHz offset frequency.