It's difficult to say really, and it is the subject of much debate in the historiography of the Klan. The film itself was visually extraordinary for its time, and made a strong impression on the people who went to see it. There are several stories of people weeping in the cinema, of fainting and even some who fired pistols at the screen. Reporting on the presentation of the film at a local theatre, one New Orleans newspaper declared: "The Birth of a Nation’ is remarkable for its power of appeal to men and women of varying processes of thought. Its sentimental side is powerful in its appeal to the heart interest, and in its representation of the more gripping historic side of the theme the production is sufficiently correct in detail as to form a strong historic interest." (New Orleans Times Picayune, March 20 1917). Wyn Craig Wade is one historian who argues quite convincingly for its influence, and has a whole chapter on the film in his study of the Klan (its quite a good read). The film was undoubtedly popular, but we cannot really know the extent of its influence. Was America already in love with the concept of the noble Klan in 1915, or was D.W. Griffiths the inspiration for this widespread feeling?
It is well known that kleagles (klan recruiters) would often hang around theatres showing the film to try and recruit those who had been inspired by the film. However, the Klan only really began to grow after 1920, nearly 5 years after the release of the film. Can we really say that a 5 year old film was the main driver of Klan growth? Although it has been argued that the film continued to be shown for several years after its release, I don't think it was the primary factor in the growth of the Klan. In my opinion, what really drove the Klan's membership drive in the 1920s were the Klan's salesmen themselves, who exploited the nation's obsession with this organization. The film was definitely important in transmitting the imagery and romance of the Reconstruction Klan, but I feel that it was the 1920s Klan's officers and salesmen who were vital to exploiting this imagery, marketing it effectively and helping to enlist millions of Americans into the order.
NB - We also have to take into account the political, economic and social turmoil that affected America in the post-WWI era (race riots, economic depression, radical agitation, renewed European immigration, etc...)