Tjukangku's work has been featured in group shows at major galleries since 2010. He held his first solo exhibition in April–May 2011, in Alice Springs. He held a second solo show at the same venue the next year, in July–August 2012. One of the works exhibited at his first solo show was bought by the National Gallery of Victoria in Melbourne. Other works by Tjukangku are held in several of Australia's major private galleries. Some of his earliest prints are displayed in the South Australian Museum.