There is no such law in the Torah stating people can't use birth control.  The Torah is the only Law that God claims is his and perfect.  Jesus tells us the only laws he gives us to follow are the two following Commandments:  Love God with all your heart, soul, mind and strength and love and treat your neighbor as you wish to be treated.  Jesus tells us these two commands cover all the law and prophets.  Jesus also warns us to not judge or condemn others unless we wish to be judged or condemned by God later on. 

So- No- Church law on birth control is not necessarily God's law and scripture does not support this belief as true or correct.