It took me a while to figure it out, so I decided to share.

DATABASES = {
    'default': {
        'ENGINE': 'sqlany_django',
        'USER': 'YOUR-USER',
        'PASSWORD': 'YOUR-PASSWORD',
        'OPTIONS': {
            'links': 'tcpip(host=YOUR-DB-IP-OR-HOSTNAME;DoBroadcast=None)',
            'ServerName': 'YOUR-SERVER-NAME',
        },
    }
}

For the sake of completeness, connecting via the regular DB API would be:

sqlanydb.connect(
    links='tcpip(host=YOUR-SERVER-HOST;DoBroadcast=None)',
    ServerName='YOUR-DB-NAME',
    uid='YOUR-USER',
    pwd='YOUR-PASSWORD'
)

It’s not hard – but tedious to tinker out.