1) Making sure these were in /etc/apt/sources.list
deb kali-rolling main contrib non-free # For source package access, uncomment the following line deb-src kali-rolling main contrib non-free
2) Making sure everything was ready
apt-get update && apt-get dist-upgrade
3) Rebooting the kernel
reboot
4) Finding out my version:
root@kali:~# uname -a Linux kali 4.6.0-kali1-amd64 #1 SMP Debian 4.6.4-1kali1 (2016-07-21) x86_64 GNU/Linux
5) Finding out which network card I had
root@kali:~# lspci | grep Wireless 03:00.0 Network controller: Broadcom Corporation BCM4360 802.11ac Wireless Network Adapter (rev 03)
6) Running this:
root@kali:~# apt-get update; apt-get install broadcom-sta-dkms; apt-get install linux-image-$(uname -r|sed ‘s, [^-]*-[^-]*-, ‘) linux-headers-$(uname -r|sed ‘s, [^-]*-[^-]*-, ‘) broadcom-sta-dkms
7) Then:
root@kali:~# modprobe -r b44 b43 b43legacy ssb brcmsmac bcma
and
root@kali:~# sudo modprobe wl
Finally you can check that it’s worked by using iwconfig and you should see that now you have wlan0 recognised by Kali Linux. Go to settings and connect to wi-fi.
Source: unix.stackexchange.com