Is there any way to measure the amount of radiation the earth receives from the sun?
Your understanding is half correct. Yes, we can measure the amount of radiation the Earth receives from the Sun.

Yes, it is difficult to get an extremely precise measure of how much radiation the Earth receives from the Sun in any one time interval. But there's not really much value in such extreme precision anyway.

However, it is fairly easy to measure solar irradiance at any one place (on earth, in the atmosphere or in space); as NASA and others currently do (kudos to farrenthorpe for the link). These measurements account for the changing distance to the sun, and the tilt of the earth, and to a very large extent the variable amount of radiation emitted from different parts of the sun's surface, because the Sun's diameter is tiny compared to the distance between the Earth and the Sun (just under 1%).

And having measured solar irradiance at one or more places, it is then easy to get a fairly precise estimate of how much radiation the Earth receives from the Sun in any one time interval.