Are regular grammars always LR(1)
No.

LR(k) grammars have to be unambiguous, that is there can be only one possible parse tree for every (valid) input. There are left- and right-regular grammars violating that, for example

$\displaystyle\qquad S \to aS \mid aaS \mid a$

or, if that one does not match your definition of right-regular, 

$\qquad\displaystyle\begin{align}
  S &amp;\to aS, S \to aA, \\
  A &amp;\to aA, A \to a
\end{align}$

as reinierpost mentions in a comment.

Of course, every regular language does have an unambiguous (right-)regular grammar; get one from its minimal DFA using the standard construction.