You can messaure it indirectly, by means of semisolid media without nitrogen. There is a good articule related: The art of isolating nitrogen-fixing bacteria

from non-leguminous plants using N-free semi-solid media:

a practical guide for microbiologists. Baldani et al. Plant Soil (2014) 384:413–431

DOI 10.1007/s11104-014-2186-6

or by amonnia production (Goswami et al., 2013).

It is different for photosynthetic and nonphotosynthetic nitrogen fixers.  Maris has rightly defined for the heterotrophic nitrogen fixers. You grow the culture in nitrogen deficient medium, If there is growth then consider the bacterium as nitrogen fixer. In heterocystous cyanobacterium, grow the culture in nitrogen deficient A and A or modified Chhu 10 with out any nitrogen sources and measure the heterocyst frquency (site of nitrogen fixation) in cyanobacterium.

initially screen on nitrogen free medium with antibiotic markers

Use non radioactive probe method (you can synthesis specific gene specific nucleotide ) -  read paper ; you can large number of colony and also accurately

use of simple nodulation test on specific plant will be more effective in screening

its  depend on type of crop and organism you r interested to study

ARA used for quantification of Nitrogen fixation by organism 

I follow what Dr. María Caridad Nápoles García suggested ....Use N free media till you get single colony

I worked with N-15 technique

You can use Arid land Ecology Lab Protocol Modified: 2010, S. Castle Acetylene reduction Assay (ARA): Measuring Nitrogenase activity adapted from Hawkes Lab.

Or the method in this paper

The potential for biological nitrogen fixing ability can be detected initially by culturing the isolates on nitrogen free media containing bromothymol blue as an indicator. Bromothymol, a pH indicator, shows yellow colour in acidic medium, green colour in neutral medium and blue colour in basic medium. during nitrogen fixation, free atmospheric nitrogen is converted into ammonia which makes the medium basic and hence turns blue (Dobereiner, 1972).