The Daily Mail claims in a recent article about the incident on January 6th:
And he [Trump] could face prosecution in state court in Washington DC for inciting the mob to violence.
Could Trump be charged with inciting the actions of 6th January 2021?
Charged: yes.
Another answer has mentioned incitement to riot in 18 USC 2101. There is also incitement to insurrection in 18 USC 2383. This carries with it upon conviction a prohibition on holding office under the United States, both in the federal law itself and also via Amendment 14 of the Constitution of the United States. There are laws under which charges could be brought, and there is certainly no impediment to bringing them after M. Trump's term of office ends. Bringing them before then raises questions of presidential immunity, but I strongly doubt that speaking at the start of a "Save America March" can be construed as an action in any official Presidental capacity.
Convicted: only maybe.
M. Trump's statements have to extend beyond what is protected by Amendment 1 and actually be incitement to insurrection. Although there is a strong case that seeking to kill the Vice President of the United States ("Where's Mike Pence?" as people shouted) and the Speaker of the House of Representatives ("Tell Nancy we're coming for her!"), seeking to obstruct the function of the Congress, and seeking to remove the Electoral College certificates, are indeed insurrection; as possibly is whatever the woman who refused to stop brandishing a knife at the door of the building was intending to do; reading the transcript of the whole speech given at the start of the "Save America March", it is difficult to point to where M. Trump specifically incited any of those things.
One can make circumstantial arguments, but the words actually uttered then and there merely encouraged marchers on a "Save America March" to march to the Capitol and cheer people on, "demand" that congresspeople "do the right thing", and "make your voices heard". This is in contrast to M. Trump's son and daughter in law who explicitly mention "fight", "fighter", and "fighting", 7 times by Eric Trump by my count and 4 times by Lara Trump. And of course Rudy Giuliani not only said "fight" but also proposed "trial by combat".
In more potential criminal trouble than even them is lawyer and prominent Trump supporter, L. Lin Wood, who explicitly called, without equivocation, several times over a period of days, on Twitter and on Parler, for the Vice President of the United States to be executed by firing squad.
There will certainly be mixed fortunes in the Trump family from this. Whilst there may be a case against Eric and Lara, and possibly Donald Sr.; Ivanka Trump did not speak beforehand that I know of, and is reported afterwards to have asked her father to go and speak to the mob about stopping, which she also did directly, albeit ineptly ("American Patriots — any security breach or disrespect to our law enforcement is unacceptable. The violence must stop immediately. Please be peaceful."), herself via Twitter for a short while.
The UK-source does not suggest what state laws he would be charged under: it may be unaware that DC is not a state. There is a Washington DC law and a federal law where it is a crime to willfully incite or urge other persons to engage in a riot, or to use something that involves interstate or foreign commerce to incite a riot. W.r.t. a federal charge, the answer hinges in part on whether he has been pardoned for offenses committed in office. Also, let us assume that the charging happens when he is out of office so that we don't have to deal with the matter of charging a sitting US president.
Anyone can be charged with inciting to riot, if there is a colorable claim that the person did incite to riot. The main legal impediment is the First Amendment. The case of Brandenburg v. Ohio rules that the First Amendment protects "inflammatory" speech. These protections
do not permit a State to forbid advocacy of the use of force or of law violation except where such advocacy is directed to inciting or producing imminent lawless action and is likely to incite or produce such action.
This tells you what fact a jury must find for a conviction. A prosecutor does not have the legal discretion to (maliciously) pursue a prosecution that has no merit.
