There are currently no diplomatic missions between Algeria and South Sudan.
However, given the Sudanese support for the Islamists in Algeria amidst the Algerian Civil War at 1990s, Algeria had distrusted Sudan and therefore had secretly supported the self-determination of South Sudan and Darfur from Sudan in response for Omar al-Bashir's supports for the Armed Islamic Group of Algeria.
This influenced the South Sudanese independence movement, notably the Sudan People's Liberation Army's leaders like John Garang, to continue the struggle against the heavily dominated Arabicized Sudanese Government, which was achieved in 2005.
Recently Algeria had shown deep concerns to South Sudan crisis and urged for mediations between two nations as part of African Union's peace plan.
[1][2] Algeria had also supported a peacekeeping mission from Japan to South Sudan.