You might try doing this in the frequency domain. The output of a Fourier Transform is orientation dependent so, if you have some kind of oriented pattern, you can apply a 2D FFT and you will see a clustering around a specific orientation.
For example, making a greyscale out of your image and performing FFT (with ImageJ) gives this:
You can see a distinct cluster that is oriented orthogonally with respect to the orientation of your yarn. With some pre-processing on your source image, to remove noise and maybe enhance the oriented features, you can probably achieve a much stronger signal in the FFT. Once you have a cluster, you can use something like PCA to determine the vector for the major axis.
For info, this is a technique that is often used to enhance oriented features, such as fingerprints, by applying a selective filter in the FFT and then taking the inverse to obtain a clearer image.
An alternative approach is to try a series of Gabor filters see here pre-built with a selection of orientations and frequencies and use the resulting features as a metric for identifying the most likely orientation. There is a scikit article that gives some examples here.
UPDATE
Just playing with ImageJ to give an idea of some possible approaches to this - I started with the FFT shown above, then - in the following image, I performed these operations (clockwise from top left) - Threshold => Close => Holefill => Erode x 3:
Finally, rather than using PCA, I calculated the spatial moments of the lower left blob using this ImageJ Plugin which handily calculates the orientation of the longest axis based on the 2nd order moment. The result gives an orientation of approximately -38 degrees (with respect to the X axis):
Depending on your frame of reference you can calculate the approximate average orientation of your yarn from this rather than from PCA.