Depends on the actual scan. A head CT can be as little as one sievert while a full blown angiogramm can be more than ten sievert. A pilot can accrue 40k flight hours over his career. If 90% of that is at cruising altitude (meaning 3-6 microsievert/hour), that would be 100-200 mSv in total. That would be equivalent to more than a hundred head CTs or a dozen angios. If you need that many CTs, your lifetime cancer risk is probably your smallest concern. But you still wouldn't expose any normal human to that level of radiation.
For general comparison astronauts are exposed to approximately 72 millisieverts (mSv) while on six-month-duration missions to the International Space Station (ISS).
According to linear no-threshold model (LNT model) the incidence of cancers due to ionizing radiation can be modeled as increasing linearly with effective dose at a rate of 5.5% per sievert, so a flight crew member receiving 200 mSv lifetime dose should have 1.1 % higher lifetime chance of cancer then general population. LNT is quite good model for high doses, but there is much less confidence for LNT at low doses, there both studies which confirm LNT at low doses and reject LNT at low doses.
For the overall US population risk of developing any cancer is 39.9% for men, 39.0 % for women.
> In terms of absolute risk, about 6.9% of flight attendant deaths were from these cancers — roughly 1 in 14. Among pilots, it was 6.7%. For the general working population, it was 5%, said the study’s first author, Dr. Vishal Patel of Harvard Medical School.
So it looks like LNT is maybe a bit too optimistic at low doses, because (with the caveat I'm not entirely sure what precisely these percentages mean) the reported excesses are 1.9 and 1.7 percentage points.
Without access to the study and study data we don't know what was measured and how it was calculated, because the value for absolute risk in general working population, the value 5%, is very different from other cancer death studies.
According the The American Cancer Society the risk of dying from any cancer is 17.2% for males, 16% for females for the overall US population.
Cosmic radiation is mainly protons and heavier nuclei. It's called radiation for legacy reasons, but it's a different beast from Earth's medical CT scans and X-rays which are manly photons.
Cosmic radiation hitting planes is also not the original cosmic protons and He nucleus etc, but secondary N and O nucleus hit by Cosmic particles creating a shower of neutrons, secondary and gamma protons, muons, pions, nuclear fragments... There's also a high dose of photons from these collisions, but proportionally it can be 500x less photons than a CT scan for a 10h USA-Europe flight.
What's biologically significant for air crew are these secondary protons and neutrons, which punch above their weight in damage interactions, they are not comparable to X-rays in Sieve alone.
Wonderful work by Mr. XKCD (Randall Munroe).
This was published in 2011 when there was "some" misinformation in the U.S. press about the Fukushima nuclear accident.
Based on this chart some proposed to use "bananas" as unit of radition (equivalent to 0.1 uSv).
So (from this chart) one flight from New York to LA exposes you to 400 bananas worth of radiation.