Here is a solution.
Note 1: TikZ is not necessary to get the desired result! (Thus, I suggest two solutions...)
Note 2: Look at A line of length \textwidth in TikZ

\documentclass[draft]{amsart}
\usepackage{tikz}
% with TikZ
\newcommand\myhline{%
\noindent\tikz[baseline=-.35em]\draw(0,0)--(\linewidth-\pgflinewidth,0);\par%
}
% without TikZ
\newcommand\myhlinewotikz{%
\noindent\rule[.35em]{\linewidth}{.4pt}\par%
}
\begin{document}
\myhline
Some Text. More Text. More Text. \par
\myhline
abc def ghi jkl mno pqr stu vwx yz. \par
\myhline
{
\LARGE\myhline
Some Text. More Text. More Text. \par
\myhline
abc def ghi jkl mno pqr stu vwx yz. \par
\myhline
}
\myhlinewotikz
Some Text. More Text. More Text. \par
\myhlinewotikz
abc def ghi jkl mno pqr stu vwx yz. \par
\myhlinewotikz
{
\LARGE\myhlinewotikz
Some Text. More Text. More Text. \par
\myhlinewotikz
abc def ghi jkl mno pqr stu vwx yz. \par
\myhlinewotikz
}
\end{document}
Edit: Here is a TikZ solution with minimized vertical spaces (without TikZ, egreg's answer is perfect).

\documentclass{amsart}
\usepackage{tikz}
\newcommand\myhline{%
\vskip-0.3\baselineskip%
\noindent%
\tikz[baseline=-.35em]%
\draw[blue,dashed](0,0)--(\linewidth-\pgflinewidth,0);
\vskip-0.3\baselineskip%
}
\begin{document}
\myhline
Some Text. More Text. More Text.
\myhline
abc def ghi jkl mno pqr stu vwx yz.
\myhline
{
\LARGE\myhline
Some Text. More Text. More Text.
\myhline
abc def ghi jkl mno pqr stu vwx yz.
\myhline
}
\end{document}
\documentclass{amsart}\usepackage{tikz,lipsum}\begin{document}\noindent \tikz[overlay,baseline]\draw(0,-0.3ex)--++(\textwidth,0) (0,2ex)--++(\textwidth,0);\lipsum[1]\end{document}