Static light scattering (some common DLS instruments that run with a cuvette or a plate have a SLS module too, which will allow Mw analysis without the need for chromatography)
Sedimentation/centrifugation method (reports Mw or Mz)
There are even more methods than these but these are the common ways. Note that each technique has its working range, limitations, and assumptions. You didn't say anything about your polymer, so I can't recommend you a particular technique. Mv by capillary viscometer (Cannon-Fenske or Ubbelohde) is an easy and cheap method that has wide applicability but requires you to know the sample concentration.
Muhammad Jawad I haven't worked with that polymer myself. However, looking at the structure online, your easiest and cheapest choice in that case would be end group titration (aka, titration of the carboxylic group with a base), which will report Mn. There is actually a paper on here that describes the procedure using potassium hydroxide as the titrant (attached below, see under Table 1).
Article Microwave-assisted Rapid Synthesis of Poly(glycerol-sebacate...
If you own a few lots with known molecular weight (such as purchased standards with certificates) and you can prepare solutions with known concentration, there is another affordable and easy alternative. You can measure the relative viscosity with an Ubbelohde Type-1 viscometer, then calculate the reduced viscosity; then plot reduced viscosity on the y-axis vs concentration (g/mL) on the x-axis and extrapolate the curve to 0 g/mL to obtain the intrinsic viscosity (ή). Now with the intrinsic viscosity and the molecular weights known, you can determine the constants α and K in the Mark-Houwink equation, which will allow you to measure future unknown samples by the same equation after you run the capillary viscosity. If you plot intrinsic viscosity vs molecular weight, the slope will give you α and the intercept will give you K.
ή = K*Mα is the MH equation where M is the molar mass of the polymer.
Know that this method works best for Newtonian fluids and most polymers are not; also that branching of the polymer will yield in inconsistent data (branched polymer and linear polymer of the same molecular weight will have different viscosities).
1H-NMR is also a possibility but there are caveats as discussed here:
Article Enzymatic Synthesis of Poly(glycerol sebacate): Kinetics, Ch...
I just want to put some addition information here. One of the benefits of size-exclusion chromatography is that you can determine Mw, Mn, and polydispersity index (PDI) with one run. It further allows quantitation of large molecular weight species and small fragments. In case you own a HPLC system but the lack of GPC software is what is deterring you from using GPC, note that you don’t really need specialized software. You can integrate a single peak in multiple (50-250) smaller peaks called “slices” and use the retention time of each slice to build a table with the molecular weights for each slice, then gain information about the averaged value across the peak. This can be built as a report template in your processing software and if you have licensed software with valid support, the supplier will be able to build that for you and send you a file to incorporate into your processing/reporting template.