
anrufen
to call
To establish contact with someone by telephone and speak to them.
Ich muss später noch meine Mutter anrufen.
I still have to call my mother later.
to call
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to call
To establish contact with someone by telephone and speak to them.
Ich muss später noch meine Mutter anrufen.
I still have to call my mother later.

to appeal to
To ask a higher authority, especially a court, for a decision or help.
Die Anwältin riet ihm, in dieser Sache das Verfassungsgericht anzurufen.
The lawyer advised him to appeal to the Constitutional Court in this matter.
'Anrufen' is a separable verb. The prefix 'an-' comes at the end in main clauses, remains attached to the verb in subordinate clauses, and in the infinitive, 'zu' stands between 'an' and 'rufen'.
Ich rufe dich heute Abend an.
I’ll call you this evening.
A common mistake is using the dative. But the accusative is always correct: you call 'jemanden' (someone, accusative), not 'jemandem' (someone, dative).
Wen hast du gestern angerufen?
Whom did you call yesterday?
When you are not calling a person directly, but rather an institution or company, the preposition 'bei' (+ dative) is often used.
Hast du schon bei der Fluggesellschaft angerufen?
Have you already called the airline?
This meaning is very formal and is used almost exclusively in legal language. In everyday life, 'anrufen' always means 'to contact by telephone'.
Nach dem Urteil entschied sie, eine höhere Instanz anzurufen.
After the verdict, she decided to appeal to a higher authority.
to reach
Erreichen and anrufen can both describe successfully making contact by phone. Erreichen emphasizes that the person you wanted to contact was actually available; anrufen refers more specifically to making the phone connection and then having the conversation. A merely unsuccessful call therefore does not mean that you have reached someone.

Ich rufe die Ärztin an und bespreche mit ihr den Termin.
I call the doctor and discuss the appointment with her.
Nach mehreren Versuchen erreiche ich die Ärztin endlich telefonisch.
After several attempts, I finally reach the doctor by phone.