This paper presents a constrained stochastic model predictive control approach for approach and landing on an aircraft carrier. Particularly, we analyze the offset recovery control for an aircraft during the powered approach-to-landing phase commonly associated with carrier based landings in the presence of stochastic wind gusts. A Dryden turbulence model is used to model the gust wind. An augmented stochastic linear time invariant system trimmed at a nominal flight condition is constructed with the gust appearing as an input. Probabilistic constraints are introduced to account for the state and control bounds. An affine disturbance feedback based control is proposed for offset recovery and glideslope regulation. This formulation leads to a tractable, sub-optimal convex approximation of the original stochastic problem and is amenable to fast online optimization solvers. The performance of the proposed approach is evaluated with numerical simulations.