Is the permission (توكيل) for the marriage of a lady over WhatsApp or a phone call valid?
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
The world is fast changing in the area of communication and information sharing. In the past, communication had been verbal or in written form on paper. In our time, electronic communications in the form of emails and text messages have replaced and are like written communication on paper.
There is a juristic principle that states:
“The written statement is considered as an oral statement.”
Therefore in response to your question, a person can seek the permission of marriage (Tawkīl) of a lady via writing text, if he is not present. This is provided that the message is communicated by a representative audibly in the presence of at least two male witnesses or one male witness and two female witnesses. 
For this to be done over the phone, complicates the matter as the offer (Ījāb), acceptance (Qabūl) and the presence of the witnesses should all take place at the same time and place. In order for this to be valid over the phone, both parties should appoint representatives who will conduct the marriage on their behalf.
Only Allah knows best
Written by Imam Abdul-Malik Sheikh
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 Al-Qawa’id Al-Fiqhiyyah by Izzat Abid al-Da’as, p52, Dar l-Tirmidhi,Beirut
 Radd al-Muhtār ‘Ala ad Durr al-Mukhtār of Imām Ibn Abidin Vol 3, P.12, Dar al-Fikr, Beirut