Under the assumption of unidimensionality (all items measure a single common latent variable), it is common to sum or average across the items to obtain a summary or overall scale score. The assumption of unidimensionality can be tested by methods of item response theory or confirmatory factor analysis for ordinal items before summing or averaging the item scores.

Before moving on to either item response theory or confirmatory factor analysis, I would first assess coefficient alpha (.7 and above) to see if the items form a reliable scale, and if so, then do exploratory factor analysis (principal factor extraction with oblique rotation) as an assessment of uni-dimensionality.