Yes, but you must have a copy of the original birth certificate. To replace, login to eCitizen portal, go to civil registration service and then select replacement of birth certificate. Fill all the details and select your pickup location in Nairobi.
If you do not have a copy of your original birth certificate or you were not born in Nairobi, then you need to visit civil registration office in your county to make replacements. If you are in Nairobi County, visit Hass plaza, 4th Floor, located in Upper Hill.