The answer is given by the conservation of momentum equation:
Q= Mproj x Vproj = Mgun x Vgun
So depending on the projectile you fire and at which velocity, you will get a certain amount of momentum to absorb.
If you want a ‘ball park figure’ (as no railguns have been fielded yet, and only experimental testing has been done): current experiments have accelerated approx. 10kg packages to approx. 3–4km/s, giving you a momentum of 30–40.10^3 kg.m/s (on average: there have been tests with bigger masses at lower velocities and vice versa).
For matters of comparison: the ballistic package for the M829 family of long rod projectiles (sabots + long rod) for the M1 Abrams MBT weighs approx. 9kg and is accelerated to approx. 1500 m/s. This gives you a momentum of 13,5.10^3kg.m/s. So our ‘average railgun’ from above would have a recoil 2 to 3 times as high as what is seen by the M1 Abrams when it fires an M829 round if you only consider the ballistic package. In the case of the Abrams you however have also additional recoil due to the acceleration of the powder charge/combustion products and the flow out of the combustion products from the muzzle. This means that in reality the recoil of the M1 Abrams is more around 20.10^3kg.m/s. So your railgun would have approx. the double of that, as it does not have any contribution from the acceleration of the powder charge and the flow out of the combustion products.
Now if the US is going to develop long range naval artillery based on railgun technology, you could expect the ballistic package to go up to minimum 30–40kg (to have the same metal hence fragment mass as a 155mm artillery projectile) and velocities in the range of 2–3km/s. This would give you a recoil impulse of approx. 80–100.10^3kg.m/s. This will normally require a recoil brake and recoil mechanism to be absorbed.