pgfplots: put a tick each first day of a month

The problem with your approach is that no expansion takes place when the option xtick={\dateticks} is processed. xtick represents a list with just one element, namely \dateticks.

One way around this is to put the picture into a macro and provide the list as an argument.

\newcommand\mygraph[1]{... xtick={#1} ...}

Now it is easy to expand \dateticks before handing it over to \mygraph.

\expandafter\mygraph\expandafter{\dateticks}

Before doing so we have to make sure that \dateticks contains the list of dates, and nothing else.

\newcommand\dateticks{2016-01-01}
\foreach \i in {2,...,12}{\xdef\dateticks{\dateticks,2016-\ifnum\i<10 0\fi\i-01}}

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\usepgfplotslibrary{dateplot}
\newcommand\dateticks{2016-01-01}
\foreach \i in {2,...,12}{\xdef\dateticks{\dateticks,2016-\ifnum\i<10 0\fi\i-01}}
\newcommand\mygraph[1]%
  {\begin{tikzpicture}
    \begin{axis}%
      [date coordinates in=x,
       xtick={#1},
       xticklabel=\day/\month,
       xticklabel style={rotate=90},
      ]
      \addplot coordinates {(2016-01-23,10) (2016-03-05,20) (2016-09-14,10)};
    \end{axis}
   \end{tikzpicture}%
  }
\begin{document}
\expandafter\mygraph\expandafter{\dateticks}
\end{document}

Edit: Here is a way to generate the ticks for an arbitrary start date and an arbitrary number of months. After executing

\setdateticks{YYYY-MM-DD}{N}

the macro \dateticks contains a list of N dates starting with YYYY-MM-DD and incrementing the month by one from date to date. E.g., \setdateticks{2016-12-01}{3} sets \dateticks to 2016-12-01,2017-01-01,2017-02-01. Here is the code defining \setdateticks.

\newcommand\dateticks{}
\newcommand\splitdate{}
\def\splitdate#1-#2#3-#4-%
  {\def\YYYY{#1}%
   \ifnum#2=0\def\MM{#3}\else\def\MM{#2#3}\fi
   \def\DD{#4}%
  }
\newcommand\setdateticks[2]%
  {\def\dateticks{#1}%
   \bgroup
   \splitdate#1-%
   \foreach \i in {2,...,#2}
     {\pgfmathtruncatemacro\mm{mod(\MM+\i-2,12)+1}%
      \pgfmathtruncatemacro\yyyy{\YYYY+divide(\MM+\i-2,12)}%
      \xdef\dateticks{\dateticks,\yyyy-\ifnum\mm<10 0\fi\mm-\DD}%
     }%
   \egroup
  }

And here is the complete code for the diagram above.

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\usepgfplotslibrary{dateplot}
\newcommand\dateticks{}
\def\splitdate#1-#2#3-#4-%
  {\def\YYYY{#1}%
   \ifnum#2=0\def\MM{#3}\else\def\MM{#2#3}\fi
   \def\DD{#4}%
  }
\newcommand\setdateticks[2]%
  {\def\dateticks{#1}%
   \bgroup
   \splitdate#1-%
   \foreach \i in {2,...,#2}
     {\pgfmathtruncatemacro\mm{mod(\MM+\i-2,12)+1}%
      \pgfmathtruncatemacro\yyyy{\YYYY+divide(\MM+\i-2,12)}%
      \xdef\dateticks{\dateticks,\yyyy-\ifnum\mm<10 0\fi\mm-\DD}%
     }%
   \egroup
  }
\newcommand\mygraph[1]%
  {\begin{tikzpicture}
    \begin{axis}%
      [date coordinates in=x,
       xtick={#1},
       xticklabel=\day/\month,
       xticklabel style={rotate=90},
      ]
      \addplot coordinates {(2016-01-23,10) (2016-03-05,20) (2016-09-14,10)};
    \end{axis}
   \end{tikzpicture}%
  }
\begin{document}
\setdateticks{2016-01-01}{12}
\expandafter\mygraph\expandafter{\dateticks}
\end{document}