Can active duty military pay local social security?

No.

Usually, the social security of active military personnel are paid by the military logistics department, active military personnel want to local social security, must wait until after the withdrawal of active duty can be transferred to the local. Active-duty military personnel retired, after the transition back to society, and can not be personal social security contributions, but need to transfer the social security relationship from the army to the local up, through the affiliated enterprises to make social security contributions. So, the active military is not available in the local social security, must wait until after the retirement or transfer.