put procedure execution into job's step
/*
CREATE PROCEDURE test
AS SELECT 1/0
GO
*/
BEGIN TRY
EXEC test
END TRY
BEGIN CATCH
--INSERT [Your Table]
SELECT
ERROR_NUMBER() AS ErrorNumber,
ERROR_SEVERITY() AS ErrorSeverity,
ERROR_STATE() AS ErrorState,
ERROR_PROCEDURE() AS ErrorProcedure,
ERROR_LINE() AS ErrorLine,
ERROR_MESSAGE() AS ErrorMessage
END CATCH