The spelling is freighted with historical significance. Traditionally, the plant and the drugs derived from it had been called “cannabis,” the scientific word for the genus of the plant itself. "'Cannabis' is the botanical term for the plant, and the term for the drug in most of the world,” explained drug policy expert Mark Kleiman of NYU in an email.
In the early 20th century “marijuana” or “marihuana” were primarily colloquial terms borrowed from Mexican Spanish, as the Brookings Institution's John Hudak explains in his book Marijuana: A Short History.
“During and especially after the Spanish-American War,” Hudak writes, “American resentment toward Mexicans and Mexican immigrants exploded.” Authorities who wanted to prohibit use of the drug soon discovered that associating it with Mexican immigrants was an effective propaganda tool.
The word marijuana — with both “H” and “J” variants — was “popularized in the United States during the 1930s by advocates of prohibition who sought to exploit prejudice against despised minority groups, especially Mexican immigrants,” explained journalist and medical marijuana advocate Martin Lee in his book Smoke Signals.
NYU's Kleiman said that “if the drug could be made to sound Mexican it would seem more dangerous.”
Starting in the 1960s “marijuana” began to be adopted as the preferred spelling in popular usage. “Marihuana” declined precipitously in the 1970s shortly after the passage of the Controlled Substances Act.
You can see the evolution of all three terms — “cannabis,” “marijuana” and “marihuana" -- in Google's corpus of English language books between the 1860s and early 2000s. In the late 19th and early 20th century, “cannabis” was the dominant term. Starting in the 1930s both “marijuana” and “marihuana” gained popularity. The use of all terms exploded in the 1960s, particularly “marijuana.”
The cause for the switch between the “h” and the “j” isn't clear. Kleiman attributes it to “people learning how to pronounce Spanish words,” but stresses he doesn't know for certain. The 70s were a time of increasing marijuana use nationwide, and many of those new users appear to have adopted the spelling with the “j.”
As for the DEA, spokesman Russell Baer told me they use “marijuana” and “marihuana” interchangeably. He said “there's no clear dividing line” between the two. The spelling used in any given document usually comes down to the preference of whoever's writing it, he said.
Asked how the DEA would respond to advocates arguing for dumping the word “marijuana” completely, Baer declined to comment.