It’s a straightforward question with a not-so-straightforward answer. I’m not any sort of lawyer, but I will borrow the classic lawyer answer of: “It Depends”.
To start, the question of legalizing cannabis – meaning its sale, distribution, and consumption is as easy as for any other good – is distinct from the question of decriminalizing cannabis, which means it’s not a criminal offense to grow, sell, or consume.
Right off the bat, we can say that the US President cannot fully legalize cannabis nationwide with the stroke of a pen, because the several states can (and already do?) have their own laws and regulations on cannabis and other drugs, parallel to the federal laws. But decriminalization is feasible, since the federal statues that criminalize cannabis are based on the drug schedules, which are regulations issued by DEA pursuant to authority granted by Congress. And that matters because most drug defendants are prosecuted under federal law.
Of course, the several states could start writing their own laws to criminalize cannabis, but that would be kinda weird since the majority of states already allow medical marijuana, and a fair number allow recreational marijuana. So re-criminalizing cannabis would repeal those rather popular laws.
So we move to how the DEA can amend the drug schedules, or how the US President can instruct the DEA Administrator. Because Congress is the grantor of such authority to the DEA and other executive agencies, and seeking to prevent regulations from whimsically flip-flopping with the passing breeze, Congress introduced the Administrative Procedures Act (APA) in 1946.
As the name suggests, the Act sets up the rules for how regulations issued by agencies shall be performed. Most of the rules mirror those of Congressional procedure, meaning that the agency must conduct hearings on proposed rule changes openly, with the opportunity for the public to submit comments. That is, regulations suddenly appearing from behind closed doors is not permitted.
Part of the rules require fixed timelines, such as a number of days for sending in comments, plus a number of days for publishing the full text of the proposed rule into the Federal Register, before the rule can become active.
Furthermore, the Act instructs the judiciary to review regulations if someone raises a challenge to the adopted regulation. Among the things the judiciary will look at is whether the regulation is improperly “arbitrary and capricious”, meaning the regulation was pretextual and is instead serving a goal outside of what Congress intended for the agency to be doing. That link describes some examples deemed to be impermissible.
If the US President issued a brief, non-explanatory executive order to remove cannabis from the drug schedules, thus shortcutting the rulemaking procedure and the period for public comment, a court challenge could arise where someone claims the regulation is arbitrary and capricious, since Congress would have expected the DEA to do a full, extensive job of considering the implications of drug availability. If the executive order does not do a similarly extensive consideration of what the DEA staff would do, then the court challenge would stand a decent chance. To be clear, the regulation via executive order would be struck down on procedural grounds, per the APA.
What if instead, the US President sternly instructs the DEA Administrator to immediately consider descheduling cannabis? This is more likely to withstand challenge, since the DEA staff would go through their normal evaluation procedure, even if it’s at an expedited rate. Thoroughness is one way to avoid being struck for arbitrary-and-capriciousness.
But there’s still a wrinkle, due to the recent demise of Chevron Deference, a doctrine where federal courts generally defer to the subject-matter experts within an executive agency if the enabling law was silent, so long as the APA’s other requirements were met. This leads to the weird possibility that a federal judge – who is unlikely to be well-versed in drug and social implications – can substitute the learned opinion of doctors and scientists within DEA with their own judicial opinion. If this sounds similar to the very arbitrary-and-capricious issue from earlier, you’d be right: a single person – in the judiciary, no less – writing regulations for drug policy is hardly what Congress intended in authoring the Controlled Substance Act in the 70s.
The overall answer is that the US President has significant sway over the DEA Administrator and can expedite the rulemaking process to deschedule cannabis, thus decriminalizing it at the federal level. But even an un-expedited rulemaking process would attract legal challenges like flies to flypaper, slowing down when the regulation comes into force. And if a federal judge decides to do so, they can outright cancel the descheduling regulation, choosing to not defer to the DEA, even if the DEA articulated their reasoning well. While it would make logical sense that such a judge must have jurisdiction over DEA, which is headquartered in Washington DC, the reality is that federal agencies can be challenged in any federal court, including ones with, uh, very outspoken opinions on federalism.
A more permanent change would be to decriminalize/legalize through Congress, since at that point, no future administration could roll that back. We’ve seen how fragile some rules or rulings can be, namely in the case of Roe v Wade being undone, as the decision was never codified into law, which would have made it much safer from judicial challenges.