In this paper, we propose a semi-definite programming (SDP) relaxation based semi-blind (SRSB) channel estimation scheme for frequency-selective multiple-input multiple-output (MIMO) multi-carrier code division for multiple access (MC-CDMA) systems. The SRSB scheme is derived from the multi-path multi-carrier decorrelator (MMD) based robust channel estimation framework developed for MIMO MC-CDMA. We formulate the semi-blind channel estimation scenario for MIMO MC-CDMA systems as a convex quadratic programming (QP) problem. Subsequently with an approximate rank relaxation this is recast as an equivalent SDP problem. Hence, the SDP solvers utilized in maximum likelihood MIMO symbol detection can be utilized to obtain the semi-blind channel estimate, thereby potentially enhancing the estimation performance without the need for additional computational resources. Simulation results demonstrate that the mean-squared error (MSE) performance of the SDP relaxation based semi-blind estimation is significantly superior compared to that of the conventional training based least-squares estimator.