Have'nt came across any report or article on their association as yet. But hypothetically they can be linked. Its a great research area to explore. Good luck.
Periodontitis has been extensively studies in relation to rheumatic diseases. Maximum literature exists for its association with Rheumatoid arthritis. Porphyromonas gingivalis is a leading pathogen in chronic periodontitis. It has been reported to produce a unique bacterial enzyme, P. gingivalis peptidyl-arginine deiminase (PPAD), which has the ability to convert arginine residues in proteins to citrulline. Protein citrullination alters protein structure and function; hence, PPAD may be involved in deregulation of the host's signalling network and immune evasion. Further, accumulating evidence suggests a role for autoimmunity against citrullinated proteins in the development of rheumatoid arthritis (RA). So the level of evidence in pathogenesis of RA is quite high.
There are quite a few association studies that have shown a higher incidence of periodontitis amongst patients with Ankylosing Spondylitis (AS) than controls. Here is one such (Keller JJ(1), Kang JH, Lin HC.. Association between ankylosing spondylitis and chronic periodontitis: a population-based study. Arthritis Rheum. 2013 Jan;65(1):167-73. doi: 10.1002/art.37746.) There are a few others too.
However, the link between AS and periodontitis has not been as deeply researched as with RA and periodontitis.
I'm totally agree with Shankar,because Periodontitis has been extensively studied in relation RA and Osteoporosis . However the relationship between Periodontitis and any of SpA has not been deeply studied.