Look at the oxidation state of reactants and products.
Hydrogen in the reactant side has oxidation state 0 similar to chlorine. In HCl, hydrogen has an oxidation state of +1, and Cl has an oxidation state of -1.
So, hydrogen moves from 0 to +1, clearly increase in oxidation state( oxidation) whereas chlorine goes from 0 to -1, a decrease in the oxidation state (reduction).
So, it is a clearly a redox reaction.