Why might a German army officer vote for Hitler?

There are many reasons as to why Adolf Hitler was voted into power:

World War I bitterness

The people of Germany were still bitter about their loss during the first World War, and this only fueled their support towards Adolf Hitler and his aggressive ways.

Promise

Adolf Hitler and the Nazi party were a sign of promise during the 1930s, as Germany suffered through the Great Depression. Almost everyone was promised something, so they supported him.

Propaganda

While the German people were not aware of how extreme things would become, culminating with the Holocaust, the Nazi party was successful in persuading the Germans that it was the Jews who were to blame for Germany's struggles.

Lack of an opponent

Opposing parties were often attacked or stayed quiet because they were scared of being murdered.