There is no such law granting natural born citizenship to the child of a U.S. citizen mother. Ted Cruz is not a natural born citizen of the United States. Ted Cruz is also not a lawful U.S. citizen, unless he naturalized as a U.S. citizen while he was an alien Canadian citizen. If Ted Cruz did not naturalize as a U.S. citizen, he is not a U.S. citizen and his service as a U.S. Senator is illegal.
Ted Cruz is not a natural born citizen but he IS a U.S. Citizen because his mother was. Being born in a foreign country does not require obtaining a CRBA at the time however one can be obtained prior to his 18th birthday. Once you attain that age you are ineligible to obtain a CRBA but must instead file a Form N-600 along with tons of documentation. This is probably what happened in Cruz case. In order for Cruz to have a U.S. Passport he needed one or the other of these documents.
Most likely a CRBA was NOT applied for at the time of birth otherwise he would have produced it. Having said that, how did he get into the US?
Ted is being his usual sneaky self about this entire thing.
In any case neither a N-600 or a CRBA confer natural born status; that is only obtained if born on U.S. Soil.
Reference: https://citizenpath.com/consular-report-of-birth-abroad/