Short Answer: No.
Long answer: No, there probably was nothing like African American architectural style in the early twentieth century.
As you noted in your question African Americans moved from the South to the North in large numbers at the beginning of the 20th century. This was largely due to the beginning of the Jim Crow era in the South. As newcomers in their communities, as well as members of a severely discriminated minority group, there were many structural impairments they faced to developing their own architectural style. For example, as others noted, the American Institute of Architects didn't license an African American to practice as an architect until 1923. His name was Paul Revere Williams, which is an amazing name in of itself, but his story is far more amazing, and worth the read.
Additionally, architecture through it's "parent" industry is a very capital intensive business. As such, it would be increasingly difficult for any community without well established roots, or deep pockets, to get a foothold in the industry. Since most of the African Americans moving north were likely former sharecroppers in the South it is hard to believe they could break into this particular industry.
It is very difficult to find information on the architectural movements of the early twentieth century outside of the major ones of: various Revival movements (I'm thinking mostly Classical, Tudor, Beaux Arts), Arts & Crafts, and the International Style. Although the last style sounds a little late for your questions timeline.
The migration did result in the Harlem Renaissance which was a huge cultural explosion driven by African American artists of all types. If there was an architectural movement to come from the migration this would be the likely birthplace of the movement. The link provided actually breaks down the various areas of art that the renaissance saw activity. One is called "Visual Art", which would presumably possibly contain architecture, but there is no mention of architectural activity. There were a growing number of African Americans that became sculptors; however, it appears that architecture was one area that the renaissance didn't extend into.
I did find an interesting post about a typical African American neighborhood in the South during the time period in question, but the houses fit within existing architectural movements of the period. Specifically, the homes would fall within revival styles. I'm not sure which, because I'm not an architecture historian by any stretch of the imagination.