Giant Rashba spin splitting was recently discovered in bismuth tellurohalide (BiTeI) [ K. Ishizaka et al., Nat. Mater. 10, 521 (2011)]. In this work, biaxial strain is used to modify the interatomic interaction in BiTeI, and the strain dependence of spin splitting is determined theoretically by first-principles density functional calculations. Large tunability is found for the Rashba energy E-R, momentum offset k(R), and coupling constant alpha(R), showing that the spin splitting in BiTeI can be significantly modified by atom-atom interaction in a solid. The maximum values of E-R and alpha(R) occur at strain eta = -1.5%. Furthermore, tensile strain is shown to favor the increase of k(R), and compressive strain favors the increase of ER. Moreover, contrast of the spin splittings between the electron at CBM and the hole at VBM reveals that E-R(e) of the electron and E-R(h) of the hole display drastically different behaviors under tensile strains. However, under compressive strains, the strain dependencies of E-R(e) and E-R(h) are interestingly similar (so are the strain dependencies of k(R)(e) and k(R)(h)). By examining microscopic electron states, the anomalous Bi-I interaction is found to be important for the spin splitting in BiTeI, and qualitative explanation for the strain dependence of the spin splitting is provided. DOI: 10.1103/PhysRevB.87.075139