When a gas is adsorbed on a solid surface, its movement is restricted leading to a decrease in the entropy of the gas i.e. $\Delta S$ is negative. Now, we know that, for a process to be spontaneous, $\Delta G$ should be negative.
We know, $\Delta G =\Delta H - T \Delta S$
Since $\Delta S$ is negative, $\Delta H$ has to be negative so as to make $\Delta G$ negative. Hence adsorption is always an exothermic process.