Is garcia cambodia safe with my birth control?

Likely: If you are talking about the produce/fruit 'garcinia cambogia' then it is likely safe to consume. If you are using an extract, as promoted by Dr.Oz, you are better off avoiding it, as he is a crook and his advice has rarely any scientific basis.

No information: "Garcinia is POSSIBLY SAFE for most people when taken by mouth for 12 weeks or less. Long-term safety is unknown. Garcinia can cause nausea, digestive tract discomfort, and headache. Special Precautions & Warnings: Pregnancy and breast-feeding: Not enough is known about the use of garcinia during pregnancy and breast-feeding. Stay on the safe side and avoid use": this pretty much sums it up.