as far as I know the pKa (=-log10(Ka)) has a very specific, thermodynamic meaning. It is the equilibrium constant of the reaction where an acid HA protonates water to give the anion A- and H3O+.
Here we have a polymer with carboxyl groups, therefore:
1. you haven't got a single substance, but a mixture of substances with different molecular weights, more or less widely distributed;
2. it is not specified how many carboxyl groups each molecule has got on, and if they are too far apart they will react indipendently;
3. the susbtances are not 'clearly' soluble in the medium, which means precipitation equilibria may interfere;
4. the concentration (if we can call it so, as it's not a proper solution) is only 0.05 g/L, pretty small even for a 'standard' organic acid with MW, say, 100 (it would be 5*10-4 M).
In these conditions my guess is that you can't determine the pKa by titration.
However, if you want to try and see what happens, the procedure is simply the following:
1. if you can, start with a more concentrated 'solution';
2. add enough strong acid (HCl?) to bring the pH to about 1-2;
3. titrate with NaOH 0.01 M or 0.001 M (remember to calibrate the pHmeter);
4. draw the titration curve.
The pKa is the pH at the point (on the titration curve) where half of your (weak) acid has been titrated, i.e. where the titration curve has a horizontal inflexion point, i.e. where its 1st derivative has a relative minimum.
Having added the strong acid, you will have a first equivalence point (where the titration curve 'jumps up'). Let's say it's at 5 mL NaOH. At that point you have your free acid ready to be titrated. Going on with the addition of NaOH, you will have another 'jump up' of the curve. Let's say it's at 15 mL NaOH. That is the endpoint, i.e. where all of your acid is converted to sodium salt. The half point is of course the mean of these two (5+15 = 20, 20/2 = 10). So you go to the x axis at 10 mL NaOH, look for the corresponding point on the curve, go from this to the value on the y axis, and that's your pKa.
As I said before, though, this method could work for 0.01 M acetic acid, but in your case you may expect hundreds of complications.
I remember reading a paper about the determination of pKa by some special spectrometric method. Maybe some physical chemist out there knows more.