I am 37 weeks pregnant. My doctor said he wants to start to stimulate the cervix as from next week. There is no infection, or... Etc. Is this normal?

Get second opinion. Without knowing the full history and the results of the obstetrician's exam there is no way to determine the appropriateness or lack thereof of this plan, but my best advice would be to get a second opinion. Good luck and hope you have a great baby.