Hitler became Kanzler by appointment from von Hindenburg on 30 January 1933, in what was supposed to be a compromise coalition government with Franz von Papen, a former failed PM, serving as vice-chancellor. That arrangement lasted about 18 months, by which time von Hindenburg had died and Roehm's SA had eliminated the majority of Hitler's opponents' leadership, then was himself killed on Hitler's orders.
That the myth of Hitler's ''election'' is so persistent is absolutely astonishing. One would think that a smart chap like Rummy had read his history at some point. Guess not.
Why? In a parliamentary system with a multide of parties (Weimar Germany being one example), ruling parties are seldom in an outright majority. They build a coalition with other parties and the now majority group gets to govern. Hitler got to the post of Chancellor the way any other Weimar politician would have, that is be part of the governing coalition where the deal includes giving the post of Chancellor to that politician.
Hitler's plurality (the largest one at the time) would have made it undemocratic not to include the Nazis or to ask him and his party to attempt to form a government. It would have been the right thing to do, but uncustomary and discriminatory.
Personally, what I find astonishing are those who continue to try to spin Hitler's election as not being "real." Hitler was as elected as anyone can be in a parliamentary system with a fragmented electorate giving rise to many, many parties.