Because my desktop computer doesn't have a wireless card, I'm tethering to my Android to connect to my Wi-Fi network.
I was wondering if Android supports promiscuous mode, so I can monitor my wireless network traffic?
IIRC you can't put an wireless interface in promiscuous mode when it's used. But this may not be true for all interfaces/chipsets/drivers.
You can install Shark for Root, which is a cut-down wireshark for Android. It does sniff on Layer 2 and above without promiscuous mode, so the results are not the same as sniffing with e.g. kismet. On the other hand you will be able to capture traffic even when tethered. It's maybe possible to set promiscuous mode on some android interfaces. Shark for Root should then be able to capture all packets that your W-LAN antenna receives.
You can't monitor your Wi-Fi network using tethering even if Android supports promiscuous mode for the Wi-Fi chipset.
Tethering does NAT internally and assigns you an IP in a 192.168.* private range via a DHCP daemon running on your phone. There's no way you can see pure Wi-Fi traffic this way.
What you can do:
Have a custom firmware installed (e.g. CyanogenMod) and do a tcpdump on your phone itself (if it supports both PROMISC mode and tcpdump)