There are a few different answers to this that all kind of build up.

• The original DEA was remnants of the defunct prohibition task forces after the repeal of prohibition; around that time some crime was committed by someone (who, if memory serves, was some form of minority, because of course in America we'll choose to galvanize against a minority) who happened to be high, and they used that as an excuse to make the drug illegal.

• The real push for it came under the Nixon administration, as a way to put his political opponents (and again, minority communities) in jail when it wasn't legal to arrest them just for being black or hippies. One of the higher-ups in Nixon's cabinet has since admitted this in an interview in 1994 that was republished around 2016; to writ:

"The Nixon campaign in 1968, and the Nixon White House after that, had two enemies: the antiwar left and black people, You understand what I’m saying? We knew we couldn’t make it illegal to be either against the war or black, but by getting the public to associate the hippies with marijuana and blacks with heroin. And then criminalizing both heavily, we could disrupt those communities; We could arrest their leaders, raid their homes, break up their meetings, and vilify them night after night on the evening news. Did we know we were lying about the drugs? Of course we did."

Thank Henry Anslinger. The first Commisioner of the Federal Bureau of Narcotics. He was strongly anti-drug and racist. In the 1930s he began a campaign that targeted Cannabis but also linked it to race and further demonized it as the cause for crime.. Look at Reefer Madness

Apart from racism and prejudice, another thing that was a big factor in outlawing marijuana was the production of hemp. The owner of a paper company, and a friend of Nixon, was concerned the production of hemp, which is arguably better than paper, would cut into his profits and run him out of business. So he lobbied his friends and started a slew of campaigns against marijuana, leading Nixon to agree, I’m assuming because it was an excellent opportunity to target black communities and the hippies, both of which he despised.

There's two key movements that lead to the ban of Cannabis in the US.

The Temperance Movement and the War on Drugs.

The Temperance Movement started in the late 19th century worked to ban addictive substances which eventually culminated in Prohibition. But Alcohol usage was only one of many things the movement targeted. The US was also dealing with a serious problem of Opiate addiction in this era.

Prior to this drugs like Cannabis and Opiates were available over the counter and were frequently mixed with other products and tonics. Coca-Cola for example originally contained Cocaine. Laws passed in this era limited the availability of many of these drugs or outright banned them.

Cannabis specifically was effectively banned in the 30s due mostly to the efforts of Henry Anslinger the first Commissioner of the Bureau of Narcotics. He ran campaigns that linked Cannabis use to violent crime in the public eye, but most of his evidence was fabricated or heavily skewed with racist overtones.

But while banned, Cannabis was not yet a serious crime.

This changed during the Nixon Administration and his War on Drugs. Cannabis use became a serious crime punishable with mandatory sentences.

After Nixon's death several Cabinet officials in his administration came forward and confirmed that the real reason for the change in policy was so that Nixon could give Police carte-blanche to arrest certain troublesome groups, most notably Blacks and Hippies, that were protesting the War in Vietnam and the Civil Rights movement.

You couldn't arrest them for protesting, but you could arrest them for using their favorite drug.

IIRC, hemp was farmed enormously in the US around the early 1900s. Rayon, developed by Dupont, was becoming commercially successful and the Duponts (along with the Hearsts who owned much of the news and advertising outlets) launched campaigns agains hemp and in favor of Rayon. So the entire hemp plant, along with the tetrahydrocannabinol-containing cannabis, were illegalized.

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