A DAC would work, just watch out for the bandwidth of the data line. How "clean" do you want your sine waves to be? If you want, say, 50 steps per period, then a 4kHz sine wave would need new values sent to it at a rate of 200 kSPS. With a 12-bit data resolution plus addressing, you're looking at a minimum of ~20 clock cycles per sample, which means you need an I2C clock speed of 4 MHz (these are all just back of the envelope calculations, you should look at the I2C interface details in the data sheet to confirm).
For AC signal generation, a parallel interface DAC would probably be a much better choice.