  We demonstrate a continuous frequency electric field measurement based on the
far off-resonant AC stark effect in a Rydberg atomic vapor cell. In this
configuration, a strong far off-resonant field, denoted as a local oscillator
(LO) field, acts as a gain shifting the Rydberg level to a high sensitivity
region. An incident weak signal field with a few hundreds of kHz difference
from the LO field is mixed with the LO field in Rydberg system to generate an
intermediate frequency (IF) signal, which is read out by the Rydberg
electromagnetically induced transparency (Rydberg-EIT) spectroscopy. Not like
resonant EIT-AT spectra, we realize the electric field measurement of the
signal frequency from 2 GHz to 5 GHz using a single Rydberg state. A minimum
detectable filed strength is down to 2.31~$\mu$V/cm and a linear dynamic range
is over 65~dB. The minimum detectable filed is comparable with a resonant
microwave-dressed Rydberg heterodyne receiver using the same system, which is
1.45~$\mu$V/cm. We also show the system has an inherent polarization
selectivity feature. Our method can provide a high sensitivity of electric
field measurement and be extended to arbitrary frequency measurements.
