Technically, yes. You are not doing any Melacha by having the already recording device record your image. However, a microphone is the same situation and we don’t use it, regardless. We don’t use electric appliances just like we don’t play music: because of Shema Yisaken Klei Shiur. Every electrical appliance is meant to be turned on or off, amongst other adjustments. Using one puts you in the mode of Issurim. Reb Moshe mentions this among other problems for using a microphone on Shabbos.
A survailance camera is not “used” by anybody, hence the Hetter. Reb Moshe, too, was Mattir to use hearing aids.