Strictly speaking, Karl Marx's specific philosophy should be termed "Marxism," as both modern Communism and Socialism diverge from his ideals in several key ways. However, Marx created the concept of communism as a political and economic theory, with his book The Communist Manifesto being his essential explanation of a communist (Marxist) society. The Communist Manifesto and the many interpretations of it fueled many revolutionary activities during Marx's lifetime, although most of these were failures; Marx in his letters explained that he didn't necessarily agree with all of his conclusions, nor of the actions and results of implementing similar systems around the world. One of Marx's most important followers was Vladimir Lenin, whose ideas helped form the Russian Revolution. Marx's ideology remains a strong political force today, and his name is either a compliment or an insult, depending on personal beliefs.
The question is somewhat complicated as it depends on what you mean by "create" and your definition of communism.
Foucault, in his frequently cited essay, "What is an Author?", talks about intellectual movements he calls "discourses", such as Marxism, Freudianism, and Christianity, which are distinguished by having an unitary "authority" to which they refer and which function as totalizing hermeneutics. Marxism, as such, acts as one of these "discourses" and is grounded in the authoritative texts of its founder, Karl Marx.
However, as pointed out by the other answerers, the term "communism" is broader and refers to some ideas created by Marx, but is not so exclusively dependent on Marx as an authoritative figure.
The term is often associated with the 1848 Communist Manifesto, which was co-authored by Karl Marx and Friedrich Engels. It combines the historical and theoretical work of Marx with Engels' detailed empirical studies of the new industrial working class in the great manufacturing towns of England. Marx himself sees his work as building on historical investigation of "agrarian communism" and application of those concepts to modern industrialized society. Earlier models of agrarian communism can be found in many Christian groups such as the Diggers and Levellers of the seventeenth century. In the twentieth and twenty-first centuries, the term "communism" is applied to Russian Leninism and Chinese Maoism, which are variations on Marx's ideas. Many countries that call themselves communist actually practice "state capitalism" or totalitarianism, which are not precisely what Marx had in mind.
Yes and no. Marx coined the term "communism," but the term "communism" has been greatly distorted and appropriated by various political leaders in history. Marx actually only wrote about communism in very small parts of his writings; his writings were mostly on topics of political economy, criticizing the economic and labor conditions of 19th century Europe. The Communist Manifesto, despite its title, does not outline what "communism" is, but rather, was meant to be a call for action for 19th century workers to reflect on exploitative labor conditions forced upon them by the capitalist class. Marx thought the capitalist economic system would eventual collapse under its own weight, and thought that "communism" would naturally replace it, but he did not know exactly a communist historical epoch would look like. As such, "communism" as written by Marx is a very vague and underdeveloped concept, something Marx himself admits. However, political leaders of the early and mid-20th century (Lenin and Mao, and later Pol Pot) developed their own ideas of what "communism" represented, which were entirely their own visions of what "communism" meant. For this reason, some say Marx was not a "Marxist" because the term "Marxist" is used to describe only those who appropriated Marx's ideas. So, yes, Marx made famous the term communism, but in practice, he is not responsible for its historical meaning or usage.