It is usually safe if the anesthesiologist is familiar putting pregnant patients to sleep. Generally you would want to do this after the 13th week

Always there is a risk for the baby. Abortion vs precipitation of delivery. If procedure is not an emergency, I believe you should wait If it's necessary and you can choose, choose a regional technique or local anesthesia.

Pregnant women should ONLY have life- or limb-saving procedures for her or for the safety of the fetus. Elective surgeries should be postponed until 6-8 weeks post-partum (birth of the baby).

Yi-Hwa Outerbridge, MD

I advise pregnant women to not have “elective” surgery. Many pregnant women have surgery for “emergent” or “emergency” reasons; for instance an laparoscopic appendectomy (because of the risk for abscess formation) or a laparoscopic cholecystectomy (because of the risk of cholangitis-sepsis). What trimester are you? It matters because you may need fetal monitoring. If at all possible, try to not get general anesthesia with a gas. It’s better to have a spinal (for a cerclage) than general anesthesia with a gas, like sevoflurane. Please consult your surgeon, anesthesiologist and your obstetrician. They all three will have a safe plan for you. You’ll do great and your fetus will be safe.