A vehicle steering control apparatus, comprising: a driving source configured to drive a driving wheel; a turning motor configured to turn a turning wheel; a backup clutch configured to be switchable between a release state of mechanically decoupling a torque transmission path between a steering operation element operated by a driver and the turning wheel and an engagement state of mechanically coupling the torque transmission path; a steering torque detector configured to detect a steering torque to be applied to a steering shaft included in the torque transmission path, when the driver operates the steering operation element; a clutch controller configured to set the backup clutch to the engagement state in starting the driving source, and to switch the backup clutch in the engagement state to the release state when the steering torque detected by the steering torque detector after the driving source starts becomes equal to or lower than a clutch release start torque that is set beforehand; and a turning motor controller configured to make the turning motor output a turning assistance torque for assisting turning of the turning wheel in response to an operation of the steering operation element, when the clutch controller sets the backup clutch to the engagement state, and configured to make the turning motor output the turning torque depending on a target turning angle in response to the operation of the steering operation element, when the clutch controller switches the backup clutch in the engagement state to the release state, wherein the clutch controller is configured to determine that shifting of the state of the backup clutch from the engagement state to the release state is completed, when an elapsed time for determination that is a period while the steering torque detected by the steering torque detector that is equal to or shorter than a predefined clutch release estimate torque is equal to or longer than a predefined SBW switch determination time, after switching of the engagement state of the backup clutch to the release state starts, wherein the turning motor controller is configured to output the turning torque depending on the target turning angle to control driving of the turning motor, when the clutch controller determines that shifting from the engagement state of the backup clutch to the release state is completed, and wherein the clutch release estimate torque is lower than the clutch release state torque. a driving source configured to drive a driving wheel; a turning motor configured to turn a turning wheel; a backup clutch configured to be switchable between a release state of mechanically decoupling a torque transmission path between a steering operation element operated by a driver and the turning wheel and an engagement state of mechanically coupling the torque transmission path; a steering torque detector configured to detect a steering torque to be applied to a steering shaft included in the torque transmission path, when the driver operates the steering operation element; a clutch controller configured to set the backup clutch to the engagement state in starting the driving source, and to switch the backup clutch in the engagement state to the release state when the steering torque detected by the steering torque detector after the driving source starts becomes equal to or lower than a clutch release start torque that is set beforehand; and a turning motor controller configured to make the turning motor output a turning assistance torque for assisting turning of the turning wheel in response to an operation of the steering operation element, when the clutch controller sets the backup clutch to the engagement state, and configured to make the turning motor output the turning torque depending on a target turning angle in response to the operation of the steering operation element, when the clutch controller switches the backup clutch in the engagement state to the release state, wherein the clutch controller is configured to determine that shifting of the state of the backup clutch from the engagement state to the release state is completed, when an elapsed time for determination that is a period while the steering torque detected by the steering torque detector that is equal to or shorter than a predefined clutch release estimate torque is equal to or longer than a predefined SBW switch determination time, after switching of the engagement state of the backup clutch to the release state starts, wherein the turning motor controller is configured to output the turning torque depending on the target turning angle to control driving of the turning motor, when the clutch controller determines that shifting from the engagement state of the backup clutch to the release state is completed, and wherein the clutch release estimate torque is lower than the clutch release state torque.