Vajna was born into a Transylvanian Calvinist family in Kézdivásárhely (today Târgu Secuiesc, Romania); then part of the Kingdom of Hungary on 4 November 1891.

He participated in World War I, as an officer in the 29th Feldjäger Battalion of the Austro-Hungarian Army, and received many honors during his forty-three months of military service.

After the German occupation of Hungary in March 1944, he maintained a good relationship between the Hungarian authorities and the arriving Gestapo and Schutzstaffel officials.

Following the Arrow Cross Party's coup, Vajna took office as Interior Minister in October 1944 and served until March 1945.

In cooperation with requests from German officials such as SS officer Edmund Veesenmayer, Vajna moved quickly to deport Jews in areas under Hungarian control to the Third Reich, where they were used as slaves and many were ultimately killed.