Are there any personality theories that use the scientific method?
What you may be interested are personality traits caught by some statistical correlations, rather than 'manually' merged by an author's intuition.
One of such tools is 16 Personality Factors.

The 16 Personality Factors, measured by the 16PF Questionnaire, were derived using factor-analysis by psychologist Raymond Cattell. This article summarizes the analysis that resulted in the 16 factors and allowed the development of the questionnaire, as well as the relation between the 16 factor theory and the popular five-factor personality theory.
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This statement has become known as the Lexical Hypothesis, which posits that if there is a word for a trait, it must be a real trait. Allport and Odbert utilized this hypothesis to identify personality traits by working through two of the most comprehensive dictionaries of the English language available at the time, and extracting 18,000 personality-describing words. From this gigantic list they extracted 4500 personality-describing adjectives which they considered to describe observable and relatively permanent traits.

(from Wikipedia: 16 Personality Factors and 16PF Questionnaire)