Catalysis of the reaction: 1-(5-phosphoribosyl)-5-imidazole-4-carboxamide = 5--1-(5-phospho-D-ribosyl)imidazole-4-carboxamide.
N-(5\'-phospho-D-ribosylformimino)-5-amino-1-(5\'\'-phosphoribosyl)-4-imidazolecarboxamide isomerase activity