user13544: To be more clear, here is a fragment of a game:
[FEN "4k3/R7/6r1/3KP3/8/8/8/8 w - - 0 1"]

1. Ra2 Rg5 2. Ra7 Rg6 3. Ra2 Rg5 4. Ra7 Rg6 5. Ra4 Rg5 6. Ra2

From the FIDE Laws of Chess:

5.5.1 d.
  The game may be drawn if an identical position is about to appear or has appeared on the chessboard at least three times (see Article 9.2).

The position of the pieces occurred three times. However the board position only occurred twice. In the first two occurrences, it was white to move. In the final position, it is black's turn. Can I claim a draw by threefold repetition in this situation?

user15874: You can claim draw if the position shows up 3 times, but it must be the same side's turn. It doesn't have to be in a row.

user18713: Yes it is considering side to move, also right of moves are also considered, for example if you lose right of castling after 3 moves repetition, you cannot claim draw or if lose right of en-passant 

user12873: You cannot claim a draw by repetition because the position hasn't occurred three times. As you noted, only that particular arrangement of pieces has occurred three times, but a position is more than just an arrangement of pieces (it involves whose turn it is).

user4418: You quote an extract from the FIDE Laws of Chess which includes the simple instruction "see Article 9.2" yet you don't bother to "see Article 9.2" where your question is answered -

9.2.1 The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not
  necessarily by a repetition of moves):
  9.2.1.1 is about to appear, if he first writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his
  intention to make this move, or
  9.2.1.2 has just appeared, and the player claiming the draw has the move. Positions are considered the same if and only if the same player
has the move, pieces of the same kind and colour occupy the same
squares and the possible moves of all the pieces of both players are
the same. Thus positions are not the same if:
  9.2.2.1 at the start of the sequence a pawn could have been captured en passant
  9.2.2.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost
  only after the king or rook is moved.

Note in particular "Positions are considered the same if and only if the same player has the move"

13544: <p>To be more clear, here is a fragment of a game:</p>

<pre><code>[FEN "4k3/R7/6r1/3KP3/8/8/8/8 w - - 0 1"]

1. Ra2 Rg5 2. Ra7 Rg6 3. Ra2 Rg5 4. Ra7 Rg6 5. Ra4 Rg5 6. Ra2
</code></pre>

<p>From the <a href="https://www.fide.com/fide/handbook.html?id=171&amp;view=article" rel="nofollow noreferrer">FIDE Laws of Chess</a>:</p>

<blockquote>
  <p><strong>5.5.1 d.</strong><br>
  The game may be drawn if an identical position is about to appear or has appeared on the chessboard at least three times (see Article 9.2).</p>
</blockquote>

<p>The position <strong>of the pieces</strong> occurred three times. However the <strong>board position</strong> only occurred twice. In the first two occurrences, it was white to move. In the final position, it is black's turn. Can I claim a draw by threefold repetition in this situation?</p>
 15874: <p>You can claim draw if the position shows up 3 times, but it must be the same side's turn. It doesn't have to be in a row.</p>
 18713: <p>Yes it is considering side to move, also right of moves are also considered, for example if you lose right of castling after 3 moves repetition, you cannot claim draw or if lose right of en-passant </p>
 12873: <p>You cannot claim a draw by repetition because the position hasn't occurred three times. As you noted, only that particular arrangement of pieces has occurred three times, but a position is more than just an arrangement of pieces (it involves whose turn it is).</p>
 4418: <p>You quote an extract from the FIDE Laws of Chess which includes the simple instruction "see Article 9.2" yet you don't bother to "see Article 9.2" where your question is answered -</p>

<blockquote>
  <p>9.2.1 The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not
  necessarily by a repetition of moves):<br>
  9.2.1.1 is about to appear, if he first writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his
  intention to make this move, or<br>
  9.2.1.2 has just appeared, and the player claiming the draw has the move. <strong>Positions are considered the same if and only if the same player</strong>
  <strong>has the move, pieces of the same kind and colour occupy the same</strong>
  <strong>squares and the possible moves of all the pieces of both players are</strong>
  <strong>the same.</strong> Thus positions are not the same if:<br>
  9.2.2.1 at the start of the sequence a pawn could have been captured en passant<br>
  9.2.2.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost
  only after the king or rook is moved.</p>
</blockquote>

<p>Note in particular "Positions are considered the same if and only if the same player has the move"</p>
