  A new class of radio source, the so-called Odd Radio Circles (ORCs), have
been discovered by recent sensitive, large-area radio continuum surveys. The
distances of these sources have so far relied on photometric redshifts of
optical galaxies found at the centers of or near the ORCs. Here we present
Gemini rest-frame optical spectroscopy of six galaxies at the centers of, or
potentially associated with, the first five ORC discoveries. We supplement this
with Legacy Survey imaging and Prospector fits to their griz+W1/W2 photometry.
Of the three ORCs with central galaxies, all lie at distances (z = 0.27-0.55)
that confirm the large intrinsic diameters of the radio circles (300-500 kpc).
The central galaxies are massive ($M_*\sim10^{11}M_\odot$), red, unobscured
ellipticals with old ($\gtrsim$1~Gyr) stellar populations. They have LINER
spectral types that are shock- or AGN-powered. All three host low-luminosity,
radio-quiet AGN. The similarity of their central galaxies are consistent with a
common origin, perhaps as a blastwave from an ancient starburst. The other two
ORCs are adjacent and have no prominent central galaxies. However, the z=0.25
disk galaxy that lies between them hosts a Type 2, moderate-luminosity AGN.
They may instead be the lobes of a radio jet from this AGN.
