I searched the internet, and found no reference to Hitler's being a Reichstag deputy or sponsoring legislation up to 1933. This tallies with my personal recollection of no such activity. A commenter found a source (John Toland's biography of Hitler) that supports an inference that he was a deputy up to 1928 (in the early days, before the Nazis' power became "national" in scope.) But there is a reason why he would have been "otherwise engaged" after 1928.
There are actually two governing "tracks" in Germany, even to this day; President, which is head of state; and Chancellor, which is the head of government.
It is noteworthy that on his first attempt at high office, Hitler ran for President (against Field Marshal Paul von Hindenburg) rather than Chancellor, winning 37% of the vote. Hindenburg remarked ironically that he had lost most of his "own" (right-wing) vote to Hitler, and had been elected by the votes of Socialists and Communists (that he despised), as the "not Hitler." (The Communist candidate, Thalman, received only three-quarters of his party's vote.)
Hitler became Chancellor, as the result of a brokered deal between himself, Hindenburg, and Franz von Papen, whom HIndenburg favored. (Von Papen was made Vice-Chancellor and given 8 out of 11 seats in the Cabinet.) But it turned out that Hitler had the upper hand, because von Hindenburg was 86 years old. Hitler was gambling, correctly as it turned out, that HIndenburg would die during his
four seven year term.
Hitler called a new round of Reichstag elections that he cast as a vote of confidence on himself. The Nazis won 44% of the vote, their highest proportion ever, and the single largest party bloc. By forming a coalition with the Nationalists (8%), they had a majority.
Hitler's next step was the passage of the so-called Enabling Act. That essentially stripped everyone of their power except the Chancellor (himself), for at least four years, making that role the supreme role. He needed a two-thirds majority to do this, but obtained it by arresting the Communists (reducing the denominator) and tricking the Catholic Center Party to support him (increasing the numerator). Once he did this, he was, in effect, Germany's Chief Executive, not Hindenburg. When Hindenburg died, he anointed himself Fuhrer. It was in this role that he addressed the Reichstag, notably in declaring war against the U.S.