As the Catechism teaches in its Part 3, Section 1, Chapter 2 sections on “The Human Communion” and “The Person in Society”, God expects us to participate in society as responsible citizens striving for the common good. There can be different ways of doing this. If we look at the examples of the saints, we see different ways to go about this.
We have the example of St. Thomas More, who went into politics and ended up defending the Church against a political ruler. There were also a number of bishops who advocated for the Church in political arenas, or pushed political leaders to help the poor or grant more righs/ less burdens/ less taxation for their flock.
We have various saints and martyrs who spoke out against politicians who were not acting according to Christian teaching. Sometimes they were martyred, sometimes they were actually able to convert the politician.
We have a number of saints who just focused on helping people who were sometimes caught up in political regimes, such as ransoming Christians captured in war, helping to restore social order after the French Revolution, helping to bring the sacraments to people or to hide priests when the Church was outlawed by some political regime (which has happened a number of times).
We have other saints who became hermits and fled the world to either pray on their own, or create better communities away from politics.
All these people were somehow “involved in politics” but in a different way.
At minimum we should be responsibly voting for candidates who we think will best promote Christian values, and we should also do things on our own to improve society, whether that’s donate to charities or sign petitions or speak out on social justice issues, etc.
If you mean "does God expect us to go join some political party, go to rallies, be active in the party, march around, go to a lot of meetings etc. " then the answer is no, only if you feel called to get that involved. We don’t all have to do that.
And in some cases, a person getting too involved in politics can actually be a distraction from God, like if they get so caught up in who wins an election that they sin, perhaps by becoming violent or angry or hateful towards the other side, or by ignoring all the other things we’re supposed to do like pray, worship and spend family time because they’re too busy having political arguments on the Internet.