Referring to the answer of @RHa
The translation
Ich fing an, politisch bewusster zu werden.
can be written more polite:
So begann ich, politisch bewusster zu werden.
For choosing the right translation, more context is needed.
Anyhow, politisch bewusst
is a very broad statement. You could mean anything with that. You could clarify your statement further.
If you began to start working for a party or march at demonstrations you would say:
So begann ich / Ich fing an, politisch aktiv zu werden.
If you started to favor left/right wing or developed your own opinion for different political topics, than you would say:
So begann ich / Ich fing an, mir eine politische Meinung zu bilden.
politically aware
exactly? Caring for the best politics? Knowing, which parties are politically active? Being aware, that politics is a distinct aspect of society? If it's all of this, thenpolitisch bewusst
in all its broadness is appropriate. If it's only one of these, then you should use other, more specific translations. – Toscho Jul 12 '17 at 19:22