  Next-generation radio surveys are expected to detect tens of millions of
active galactic nuclei (AGN) with a median redshift of z > 1. Beyond targeted
surveys, the vast majority of these objects will not have spectroscopic
redshifts, whilst photometric redshifts for high-redshift AGNs are of limited
quality, and even then require optical and infrared photometry. We propose a
new approach to measure the redshifts of lobed radio galaxies based exclusively
on radio-frequency imaging and broadband radio photometry. Specifically, our
algorithm uses the lobe flux density, angular size and width, and spectral
shape to derive probability density functions for the most likely source
redshift based on the Radio AGN in Semi-analytic Environments (RAiSE) dynamical
model. The full physically based model explains 70% of the variation in the
spectroscopic redshifts of a high-redshift (2 < z < 4) sample of radio AGNs,
compared to at most 27% for any one of the observed attributes in isolation. We
find that upper bounds on the angular size, as expected for unresolved sources,
are sufficient to yield accurate redshift measurements at z > 2. The error in
the model upon calibration using at least nine sources with known spectroscopic
redshifts is <14% in redshift (as 1 + z) across all redshifts. We provide
python code for the calculation and calibration of our radio continuum
redshifts in an online library.
