The question is more complicated than it seems.
Even though it is easy to agree to that some people are more competent in their social behavior than others, it has proven to be very difficult to define what we mean when we talk about social skills (or "social intelligence", "social competence"). Is it the ability to manage social relationships, does it contain empathy, is it the knowledge about how social relationships work, the number of friends, or being good in negotiations, as you define it? Over the years, researchers have used partly overlapping and partly distinct definitions. For the difficulties associated with conceptualizing social intelligence refer to this review by Kihlstrom and Cantor (2000).
Consequently, this difficulty is also reflected in the difficulty of measuring social skills. A wide variety of measures have been developed. Based on the multitude of conceptual approaches it is clear that the results of these measures will often diverge. For example, Riggio et al. (1989) conducted a study in which participants completed a large number of standardized measures of social intelligence. The measures included tests that measured the ability to perceive the feelings and intentions of others, the ability to assess interpersonal relationships, various measures aimed at testing the ability to predict social behavior of others and the ability to perceive feelings of others. The correlations of these measures "ranged from -0.20 to 0.44, with a mean r of 0.20". Thus, they had some overlap among each other, but this overlap was pretty low. Riggio et al. also measured academic intelligence (with a variety of measures) and found that "the measures of academic and social intelligence ranged from -0.10 to 0.52, with a mean r of 0.15". Some have used results like these to question the usefulness of social intelligence as a construct. Others have questioned whether it is possible to distinguish social from other forms of intelligence at all. The methodological problem becomes even clearer if you keep in mind that most social intelligence tests are based on paper-and-pencil (self-report) questionnaires that do not necessarily overlap with peer reports or actual tests of social skills (in an assessment center, for example). In light of these difficulties, it may not be surprising that a prominent review of the literature regards the search for "social skills" as a concept as "long, frustrating, and fruitless" (Landy, 2005).
Even though the field does not seem to have found consensus in the mean time, more recent research shares the idea that it is necessary to take the multidimensionality of social intelligence into account when conceptualizing and measuring them. From this perspective, there will be elements of social intelligence that have a stronger overlap with "pure reasoning" measures of IQ than others. For example, Jones and Day (1997) found in research with sample of high school students that indicators of "crystallized social knowledge" (declarative and procedural knowledge about social events) were highly correlated (r=.79) with academic problem solving (which is closely to related to what is measured with classic IQ tests). However they were not so strongly related (r=.29) to "social-cognitive flexibility" (the ability to apply social knowledge flexibly to solve novel problems). A strong point of this research is that the researchers combined self-ratings and tests with teacher ratings to assess all of these constructs. These findings suggest that some parts of social intelligence (social knowledge) are virtually indistinguishable from general intelligence. However, other elements of social intelligence (applying social knowledge) are somewhat positively related to intelligence (more intelligent = somewhat better in social problem solving on average).
Jones, K., & Day, J. D. (1997). Discrimination of two aspects of cognitive-social intelligence from academic intelligence. Journal of Educational Psychology, 89, 486–497. doi:10.1037/0022-06220.127.116.116
Kihlstrom, J.F, & Cantor, N. (2000). in R.J. Sternberg (Ed.), Handbook of intelligence, 2nd ed. (pp. 359-379). Cambridge, U.K.: Cambridge University Press.
Landy, F. J. (2005) The Long, Frustrating, and Fruitless Search for Social Intelligence. In K. R. Murphy (Ed.) The Emotional Intelligence Bandwagon: The Struggle Between Science and Marketing for the Soul of EI. Mahwah, NJ: Lawrence Erlbaum and Associates, 2005
Riggio, R. E., Messamer, J., & Throckmorton, B. (1991). Social and academic intelligence: Conceptually distinct but overlapping constructs. Personality and Individual Differences, 12, 695–702. doi:10.1016/0191-8869(91)90225-Z