As already stated in another answer, the Kardashev scale was interpolated by Carl Sagan to admit non-integer values. The formula would be the following:
In this formula, K is the Kardashev's rating and P is the power the civilization uses, in Watts. This actually means that we could rate whatever civilization we want: the power will never be negative, so the logarithm in base 10 of it will always be defined. Given this scale, we can establish the minimum on a civilization of type -0.6.
Wikipedia states that:
World energy consumption refers to the total energy used by all of human civilization.
Typically measured per-year, it involves all energy harnessed from every energy source we use, applied towards humanity's endeavors across every industrial and technological sector, across every country. Being the power source metric of civilization, World Energy Consumption has deep implications for humanity's social-economic-political sphere.
As for that,
- A prehistoric civilization will have an almost 0 energy consumption (the only energy source is fire), and thus will be a civilization of type -0.6.
- A civilization of type 0 will consume about 10^6 Watts.
Since the industrial revolution, the data of the world consumption is available:
(Credit to http://ourfiniteworld.com/2012/03/12/world-energy-consumption-since-1820-in-charts/)
The ~20 EJ/year on 1820 are about 0.63 TW = 6.3 * 10^11 W. That is a civilization of type 0.6.
All that data means that if you can approximately determine the energy consumption of your civilization, you can give it a value in the Kardashev scale.