If you know the radioisotope that you are detecting then you can use the gamma constant to relate radioactivity to absorbed dose and effective dose.
Be cautious, first you have to determine the relation between count rate and activity. It´s not trivial because of geometric effects, efficiency and kind of radionuclide. You have to take care with dead times because of saturation count losses by the special counter you use. If you want to check this behaviour of your counter use a strong source and go closer and closer with your counter. You will certainly experience constant count rates in contradicction to inverse square law.
If you have found a reliable and quantiative relation between count rate and activity you can use gamma constants for gamma emitting radionuclides or beta conversion factors for beta emission.
I agree with Hanno's detailed answer . The other answers are correct in stating that the GM can be calibrated for absorbed dose or effective dose. The GM will be calibrated only for the calibrating conditions. Nevertheless, GM detectors have been used extensively for dose or dose approximation and are acceptable for radiation protection situations. They can be used for dose of record only after calibration.
I would like to build on Hanno's great reply. A GM could be calibrated so that the number of detected events from photon irradiation (which is directly related to the photon fluence rate that the detector is exposed to) can be related to absorbed dose to some material (such as tissue or water) if charged particle equilibrium (CPE) exists at the location of measurement. Under conditions of CPE, absorbed dose is equal to the photon fluence multiplied by the photon energy multiplied by the mass energy absorption coefficient (I won't derive this relationship - please check a text book such as Turner's Atoms Radiation and Radiation Protection).
Here's the practical part. Photons in the range of about 300 keV to a few MeV predominately interact by Compton Scatter. Since Compton scatter is relatively energy independent in this energy range, you could calibrate a GM to, for example, Cs-137 to absorbed dose (satisfying the CPE equation I gave above) and, within an error of a few percent, could use this conversion constant to also predict a GM's absorbed dose from photons at other photon energies also between 300 keV to a few MeV.
That is, a GM calibrated to convert the rate of detected events from a Cs-137 source into absorbed dose to some material (usually water) can be used to predict the absorbed dose to that material from another isotope such as Co-60 (to within a few percent). the important thing to keep in mind is that this rule of thumb falls apart below 300 keV where photoelectric absorption (which is highly energy and material dependent) and above a few MeV due to increased pair-production probability.
You'll notice that I reference photons and not beta's (or other charged particles). You didn't specify any specific type of radiation, but without going into Cavity theory (please see Attix for an excellent explanation), the approach above is not applicable for measurements of charged particles made in air.
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