This raises another question. What difference does splitting ground planes make if analog and digital ground pins of the IC are connected internally?
I have attached a closer picture of the ADC, The red line shows the digital ground pin is not connected to the analog ground pins at all. However I do realize that this doesn't matter if they are internally connected 
if they are connected internally how is it possible to prevent the SPI return current from coupling with the ADC analog current then?
The answer is that you separate out the return current paths. A split/single-point-connected ground plane is kind of a shortcut way of enforcing this, but only really works on eval boards with one mixed signal IC, limited supporting circuitry, and limited external connections. In the context of a more complex design, it falls onto the designer to ensure that return currents are properly directed, regardless of how the ground plane is laid out. A big part of this is placement (in fact, good layout in general is 90% about good placement), so making sure you have a good idea of what kinds of currents will flow in/out/between each block of circuitry and place them accordingly is a good start. From there, consider the loop paths between blocks, and make sure you route accordingly, including maintaining a solid ground plane as much as possible.
There are multiple loops to be concerned with here. This starts with the power supply input, which is a loop unto itself between your input capacitors (I don't see any on your board, btw) and the external power source. From there you have a loop between the bulk capacitors on the board to the local decoupling caps. Then you have the loops formed by decoupling caps with the ICs they serve, these want to be as tight as possible to provide maximum stability of the local power supply, and they are the foundation of the next set of loops, which include the signal tracks between ICs. Consider that when your MCU is clocking the SPI line to the ADC, on every clock transition the MCU delivers a pulse of current into the clock line. The energy for that pulse comes from a local decoupling cap at the MCU, delivered through the MCU's output stage into the clock line, into the ADC, and is returned through the ADC's ground pins, through the ground plane, back to the MCU decoupling capacitor. High frequency return currents will be concentrated in the path of lowest inductance. When a signal track is routed over a continuous, unbroken ground plane, the lowest inductance return path is through the ground plane directly underneath of the track. This is why a continuous ground plane is generally ideal, because return path inductance is minimized (as is the DC path resistance by virtue of there being as much copper as possible). In terms of 'high frequency', remember that with digital signals it's not the transition frequency but the transition rate (slew rate, dV/dt) that determines the highest frequency of concern. This is why you don't want to route tracks across a break in the ground plane, because it forces those return currents to detour through a higher inductance path around the break to get where they need to go. This is also what makes the old advice to only have one point of connection between analog and digital grounds tricky--in order for that to work properly, any signal that crosses the digital/analog boundary has to do so at that single point. Having a single contiguous plane is often a more realistic path to acceptable results.
Even if your design would benefit from a split ground plane strategy, that would likely only come into play after you've dealt with other things that will have a much more significant effect on your precision: power supplies, input filtering (power and signal), DAC/ADC reference quality, error terms in your analog components, etc. No amount of fancy ground plane shenanigans will make up for deficiencies in those areas, but they will all benefit from a good ground plane.
In any case, aside from the fundamental question of whether or not you should split your ground planes, your ground planes are far too fractured by signal tracks to really be of any benefit here. You have a number of islands, and near-islands in the ground pours as things stand now. You could probably get a reasonably contiguous plane with two layers on this design, but it will take much more careful routing and you'll still likely need to stitch top and bottom pours together with vias. In general, I suggest moving a lot of your longer tracks to the top layer, and rather than moving whole tracks to the bottom layer, use short bottom-side tracks to allow signals on the top layer to cross. The small hole created in the ground plane by a short jumper track is far less harmful than a big slot created by a longer track. Where you must have longer tracks on the bottom, avoid having top side tracks cross over them. If that can't be avoided, use a top side pour and stitch it to the bottom pour, such that the top and bottom pours add up to a more-or-less uninterrupted plane.
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