加わる
くわわる · kuwawaru · JLPT N3 · verb-godan
to join in
加 = add; 加わる = to get added, so you join in (加える = to add something)
加 is the kanji for add, as in 追加 (addition). The -aru ending makes the verb intransitive: 加える means you add something, while 加わる means you yourself get added to a group. Compare 変える/変わる and 終える/終わる.
加 — force 力 + mouth 口
加 is traditionally analyzed as a compound of 力 (strength) and 口 (mouth), suggesting boasting or exaggerating one's effort with words. From this it extended to the meaning 'to add' or 'increase'. Today it is used broadly for addition, both literal and figurative.