Well, yes and no. That is the short answer, but not a satisfying one.
One of the key questions in the early years of creativity research was whether creativity should be studied on its own, or as a component of intelligence. After some studies, consensus was that intelligence and creativity, although somewhat related, are distinct enough to be studied on their own.
For now, research says yes, you need some intelligence to be creative, but after a certain threshold, creativity and intelligence are no longer related.
However, a meta-analysis suggests that there is very little relationship between intelligence and creativity, and that people with a relatively low intelligence score can be creative.
The common sense answer is that it depends on the field in which you want to be creative in. Artistic creativity is not as dependent on intelligence as, say, creativity in the physics or medical fields. To be creative in a particular field, you need to be knowledgeable in that field, which presupposes a level of intelligence.
Other factors also influence how creative you are. Most researchers agree that the curiosity and openness to experience that goes with the Big Five Personality factors Openness to Experience and Extraversion are strong predictors of intelligence.
Robert Sternberg goes as far as to say that creativity is a decision, that if you decide to be creative, you will be more creative, provided that you believe the decision to be creative will be rewarded, not punished.
Sources
Furnham, A., & Bachtiar, V. (2008). Personality and intelligence as predictors of creativity. Personality and Individual Differences, 45, 613-617.
Kim, K. H. (2005). Can only intelligent people be creative? A meta-analysis. The Journal of Secondary Gifted Education, vol. 26, no. 2/3, 57-66.
Sternberg, R. J. (2006). The nature of creativity. Creativity Research Journal, 18(1), 87-98.
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