Yes, that is considered a possibility by some. See this paper, entitled "The Phenomenology of Right Handed Neutrinos".
Section 6 of this paper specifically considers the possibility that sterile neutrinos (i.e., right-handed neutrinos) may constitute dark matter.
Left-handed neutrinos are ruled out as dark matter candidates because their “free streaming length” is not consistent with observed large-scale structures in the cosmos. “Free streaming length” is the average distance a particle travels before falling into a potential well https://conferences.fnal.gov/dmwksp/Talks/Kaplinghat.pdf.
Right-handed neutrinos have never been observed. This is a bit odd, because neutrinos are fermions, and all other fermions occur in both right- and left-handed forms. So, if right-handed neutrinos do exist, there's got to be a reason we haven't observed them. Some possible reasons are: A) they interact even more weakly than left-handed neutrinos; B) they are too massive to be produced in significant numbers by the types of interactions we see going on in the universe and the lab now.
Theory doesn't give a lot of help. Different interpretations suggest that right-handed neutrinos (if they exist) may have masses anywhere from zero to somewhere above 10^9 GeV. By comparison, the mass of a proton is roughly 1 GeV. The only evidence available at the time this paper was written (2013) was woefully insufficient to conclude anything about the actual mass of right-handed neutrinos (if they exist).
As the author states, “Sterile neutrinos are collisionless and can be very long lived, hence they are an obvious DM [dark matter] candidate. This scenario has been studied by a large number of authors, ...”. It is expected that right-handed neutrinos will come in several types having a range of masses, which allows for fine-tuning of theoretical models until/unless the masses are known.
The author's concluding paragraph starts with “Right handed neutrinos provide plausible explanations for neutrino oscillations, the observed dark matter and the baryon asymmetry of the universe, which cannot be understood within the SM[Standard Model].”
So, the OP's guess that dark matter might consist of right-handed neutrinos is entirely reasonable.