Isn't there any relation to calculate the dipole moment from the electronegativities of the participating atoms?

what i can think of is of no direct relation but u can calculate percent ionic charcter of bond and by knowing the bond length the dipole moment can b found

like percent ionic character in say AB is given as 16(electronegativity difference between two atoms) + 3.5(difference)^2 say it is x percent 

then dipole moment /ideal dipole moment x100 = x

ideal dipole moment = bond length x charge on electron

ie if bond length is in angstrom and charge in esu the dipole moment comes out in debye

eg. if difference between HCl molecules is thaken as 0.9 the percent character is 17.23

so now bond length is 1.275A then dipole moment is 

= 17.23/100 x 4.803x 10^-10 x 1.275 x 10^-8

=1.05 D whichid the dipole moment of HCl bond

There is a very simple formula here :-

 16(X_A-X_B)+3.5(X_A-X_B)²  where X is electronegetivity.