The short answer is: someone who is a potential victim of racism, who is part of a group that is commonly discriminated against.
The long answer is difficult to write because this is a fairly recent expression, with a heavy cultural context. My answer is exclusively about France, I have no idea how or even whether this word is used elsewhere.
The word racisation was coined by French sociologist Colette Guillaumin in the early 1970s. (The first occurrence on Google Books is from 1978 but Google doesn't have the earliest uses.) It designates the sociological process by which certain people tend to find themselves victims of discrimination because they are members of a minority group. The concept is not limited to what is commonly called race in French or race in English today, which tends to focus on skin color.
The suffix -ation is a common noun formation suffix, starting from a verb ending in -er. The suffix -iser is a common verb formation suffix designating a transformation process of some kind. Thus raciser would be the process of transforming a social structure into one that involves a concept of race, and racisation would be the noun for this process. However, as far as I know, the noun racisation appeared before the verb raciser which hasn't really taken off. Given that the suffix -ation is very productive, this is unexceptional.
The adjective racisé (which would be the past participle of raciser) is a more recent addition to French. Its history is fairly well covered in the French Wikipedia article on racialisation. I think some activist groups started using it in the late 2000s or early 2010s, and it started to reach somewhat mainstream use in the late 2010s. To give an idea of its spread, the Wiktionary article was created in July 2016, and the reference dictionary Le Petit Robert added it in its 2018 edition.
Exactly which groups count as racisé depend on who you ask. Women don't: a woman who is a victim of racism would be une femme racisée. LGBT+ don't either, at least with most people who use the term. Groups that focus on certain specific discriminations may or may not get on with groups that focus on other discriminations.
The political context of racisé is that until 2017–2018, it was essentially only used by groups that have a racialized approach to discrimination issues: (certain) minorities must form autonomous groups that make their own struggle against the majority group. This is relatively unusual in the French political tradition. The history of struggle against discrimination in France is dominated by an egalitarian approach: I may look different, eat different food, have a different accent, but I'm a human being and a citizen just like you and you should treat me the same way, give me the same education, let me have the same jobs and live in the same places. Positive discrimination (which is how most French people perceive affirmative action) is not an established concept in France (apart from gender equality, and even that is recent). Minorities have traditionally sought integration, and left-wing political groups have traditionally promoted integration and joint struggle.
In the 2010s, there has been a rise of groups of minorities promoting a communitarian approach (communautariste). Such groups entered the news in 2017 with reports of meetings that were only open to members of certain visible minorities. This has met some backlash from other groups that defend the rights of minorities but oppose racial discrimination whether negative or positive. In 2017, using the word racisé labeled you as a member of a visible minority who rejected the French tradition of integration and promoted what many would consider as a racist approach, and labeled you as a political activist.
The connotations of the word are evolving rapidly. In 2019, merely using it is not such a strong political marker as is was even two years ago. It's entirely possible that the author of this tweet is not involved in politics. It's still an age marker; I suspect that it's fairly common among people who are students in the late 2010s but a lot less common among older people.
