A scheme for realizing Thirring vector solitons is proposed, with the help of giant Kerr nonlinearity and electromagnetically induced transparency in an atomic gas system. Generic Thirring vector solitons, formed by the distributed nonlinearity coupling and loss (or gain) coefficients, are constructed analytically, using the homogeneous balance principle and the F-expansion technique. Unlike previous studies, our results demonstrate that the Thirring vector solitons can be manipulated and controlled by changing the nonlinearity coupling and the loss or gain parameter along the propagation distance.