GRANT EXEC ON [sp_start_job] TO [someUser]
By default, members of the sysadmin fixed server role can execute this stored procedure. Other users must be granted one of the following SQL Server Agent fixed database roles in the msdb database:
For details about the permissions of these roles, see SQL Server Agent Fixed Database Roles.
Members of SQLAgentUserRole and SQLAgentReaderRole can only start jobs that they own. Members of SQLAgentOperatorRole can start all local jobs including those that are owned by other users. Members of sysadmin can start all local and multiserver jobs.