Short answer: No.

Longer answer:

• Hitler spent his whole life ranting and raving about ‘Marxism,’ for him a catch-all term for social democrats, socialists, communists, trade unions and the entire left.
• Before coming to power, the Nazi Party spent its entire existence engaged in bitter street fights, with the left and the workers’ movement. Not only were the Nazis not part of the socialist movement. They were killing socialists in the streets, and that was their main function.
• After coming to power, the Nazis immediately banned the social democratic and communist parties, dissolved the trade unions, and filled the concentration camps with left-wingers.
• During World War Two and the Holocaust, socialists were one of the groups they targeted for mass murder, for example through the infamous ‘Commissar Order’ of 1941.

 But why did the Nazis (National Socialist German Workers’ Party) have ‘socialist’ in their name?

• They didn’t. They had National Socialist in their name. National Socialism was a distinct ideology, deliberately counter-posed to socialism. One of the things Hitler hated about socialism was the fact that it was internationalist.

Why did they have ‘Workers’ in their name? Was their party made up of workers?

• They were definitely not a workers’ party. Their members and voters were small business owners, students and farmers. Even in the early 1930s when their movement was on the cusp of power, they controlled every students’ union in Germany but by contrast, their membership and activity in the factories were extremely feeble.

When the Nazis were in power, did they bring in socialist policies?

• If socialism is workers’ control over industry, they didn’t bring that in. In fact they destroyed workers’ power by dissolving trade unions and political parties.
• If socialism means seizing the wealth of the rich, then no, they didn’t do that either. Jewish people were brutally dispossessed but Jewish people made up the tiniest part of the rich in Germany.
• If socialism means regulation of business, public works programmes (the Autobahn) and state borrowing and spending, then sure, the Nazis did that. But we see similar policies in pretty much all capitalist countries during the 1930s to combat the Great Depression.
• These days we have a lot of extreme free-market libertarians who believe that any state regulation or public spending is ‘socialism.’ It is only possible to argue that Nazi policies were socialist if you’re using that definition – a definition so broad it’s meaningless.

Did the Nazis call for socialist policies before they came to power?

• Yes. But they promised everything to everyone. To the rich, they promised to end strikes and prevent a revolution. To the poor, they promised to ‘take on the capitalists and the Jews.’
• Like some political forces today, they had this whole ‘Neither left nor right’ shtick – ‘neither capitalism nor socialism but a third way.’ But what it actually boiled down to was capitalism with more parades and more genocide. They did not make deep changes in the socio-economic sphere of society.  
• The Jews suffered 12 years of persecution and mass murder. But the capitalists got lucrative state contracts and a cowed workforce.
• Many of the Stormtroopers (the Nazi street-fighting paramilitary movement ) believed they were fighting for some kind of wealth redistribution. In other words these particular Nazis were high off their own supply.
• After 1933 the Stormtroopers got impatient. When were they going to ‘take on the capitalists?’ The answer was: never. In the ‘Night of the Long Knives’ Hitler put the Stormtrooper leaders up against a wall and shot them. 

So in conclusion..?

The Nazis were liars. They believed that, since their enemies were all-powerful and evil, they were justified in lying. They called it ‘Nordic Cunning’ and they delighted in it. They thrived by muddying the waters with blatant lies (the bigger, the better) and a constant barrage of bad-faith arguments. What they said today contradicted what they said yesterday, and it didn’t matter. When they promised wealth redistribution and ‘taking on the capitalists,’ they were lying. When they used words like ‘socialist’ and ‘workers’ that was more good old ‘Nordic Cunning.’

A lot of the confusion they so carefully sowed is still with us. Don’t fall for it.

The above is mostly drawn from three books I highly recommend:

• The Coming of the Third Reich by Richard J Evans, Penguin Books
• The Oppermans, by Lion Feuchtwanger, Persephone Books
• And Red is the Colour of Our Flag, by Oskar Hippe