This paper explores a metric-affine generalization of the gravitational sector of the Standard Model Extension (SME) within the framework of spontaneous Lorentz symmetry breaking (LSB). The authors derive modified Einstein field equations to obtain a new axisymmetric vacuum spinning solution for a specific bumblebee profile. This solution incorporates the effects of LSB through a dimensionless parameter \( X = \xi b^2 \), where \( \xi \) is the nonminimal coupling constant and \( b^2 = b^\mu b_\mu \) is the vacuum expectation value of the bumblebee field. When LSB is turned off (\( X = 0 \)), the solution reduces to the Kerr metric, as expected. The paper also calculates geodesics, radial acceleration, and thermodynamic quantities for this new metric. Additionally, an upper bound for \( X \) is estimated using astrophysical data on the advance of Mercury's perihelion. The study provides insights into the impact of LSB on gravitational phenomena and the behavior of black holes in alternative theories of gravity.This paper explores a metric-affine generalization of the gravitational sector of the Standard Model Extension (SME) within the framework of spontaneous Lorentz symmetry breaking (LSB). The authors derive modified Einstein field equations to obtain a new axisymmetric vacuum spinning solution for a specific bumblebee profile. This solution incorporates the effects of LSB through a dimensionless parameter \( X = \xi b^2 \), where \( \xi \) is the nonminimal coupling constant and \( b^2 = b^\mu b_\mu \) is the vacuum expectation value of the bumblebee field. When LSB is turned off (\( X = 0 \)), the solution reduces to the Kerr metric, as expected. The paper also calculates geodesics, radial acceleration, and thermodynamic quantities for this new metric. Additionally, an upper bound for \( X \) is estimated using astrophysical data on the advance of Mercury's perihelion. The study provides insights into the impact of LSB on gravitational phenomena and the behavior of black holes in alternative theories of gravity.