You heard almost right: It's not electromagnetic force as such, but electromagnetic energy. You already know the equation:
E = m c²
If you take the amount of chemical or electromagnetic energy stored in, say, a car battery (about 45 Amp-hours at 12 Volts):

45 Amp-hours times 12 Volts = 540 Watt-hours = 2,000,000 Joules (roughly)
and convert that to mass (using mass = E/c², and the definition of Joule = kg*meter²/c²⁶ kg*meter²/s²) / (3*10⁸ meter/s)² = 2*10^(-11) kg = 2*10^(-14) g.

You find that the energy stored in a car battery adds 20 femtograms to the car. For comparison, that's about 1/5 of the mass as a 1-atom thick slice from one of your own hairs. The gravitational force of so little mass is immeasurably small.

I chose a large example (a car battery with a lot of energy) because this shows how amazingly little gravity is exerted by pure energy (whether chemical or electromagnetic). To take another example, the total sunlight hitting Earth at any time is 10¹⁷ Watts. By the same calculations above, you find that each second of sunshine adds only about 1 milligram of mass to Earth. All that electromagnetic energy, and yet it causes so little gravity!

Yes, the formula exists: it is none other than the famous E = mc².

So, if you want to know how much gravity an electromagnetic field makes, and then takes the energy contained in that field, plug it into the equation, solve for m, and calculate the mass. You can then use Isaac Newton's gravity equation (F = G*m1*m2/r²) to approximate the gravitational force this energy will exert. Note that Newton's formula *is* an approximation. Einstein's theory of general relativity provides a re-working of the theory of gravity, but the math behind it is more sophisticated than anything I know.