We have studied the correlation between the elastocaloric effect and the crystallographic direction where a uniaxial stress is applied in a textured polycrystalline Ni-Mn-In-Cr ferromagnetic shape memory alloy; this alloy displays martensitic transformation around room temperature and presents an L21 cubic structure in the austenite phase. The texture in the material was induced by simple arc melting synthesis; using inverse pole figures, a favored grain growth was shown in the direction [001] perpendicular to the cooled surface. The elastocaloric effect was determined by direct measurements of the adiabatic temperature change (ΔTadme), while compressive stress was applied and released; hereby, it has been shown that it is possible to exploit the columnar growth texture in order to obtain a large and reversible elastocaloric effect. The reversible elastocaloric response was measured between 280 and 310 K by applying moderate stresses of 50, 75, and 100 MPa in the [001], [111], and [011] directions. A strong interrelation was found in the cyclic ΔTadme values of −3.9, −2.0, and −1.3 K after unloading a compressive stress of 100 MPa applied mainly in the [001], [111], and [011] directions, respectively.