The op-amp you are using is not a single-supply type. It can only reliably deal with voltages in the range of about Vee+3 to Vcc-3, with a single 12V supply that is about 3V to 9V. The output range is similar (the output cannot go all the way to ground or all the way to Vcc).
The output of the DDS chip is typically 0.037V to 0.645V, so it is way outside the allowable common mode input range for that particular op-amp when it is operated from a single 12V supply.
If you are okay with having a bias of G\$\cdot\$ 304mV (where G is the gain) in the output then you can use the digipot as shown, however you will need to use an op-amp that has an input common-mode range that includes the negative supply (and you also probably want one that has an output that can swing close to the negative supply rail).
So, look for a "single supply" op-amp or a RRIO (rail-to-rail input-output) op-amp that can work from 12V and meets your other requirements. RRIO will definitely work however performance may be inferior in subtle ways (such as distortion) compared to a single supply. Or not, since your application will likely leave half of the complex RRIO front end unused due to the low maximum input voltage.