Yes, TIG welding is possible with both AC and DC current machines. But in the case of DC, it is better, that the user or welder should have some experience of tig welding. Because you will need to adjust the DC welder properly before using it for aluminium welding.
Basically, during aluminium welding, when the metal gets exposed to the environment it creates aluminium oxide. Aluminium oxide has a higher melting point than aluminium and this is the hindrance in creating a bond between two parts for welding. AC TIG machine has more penetration in welding the aluminium and creates more heat to give a strong bond between metals. It also cleans the aluminium oxide layer.