One way to do this is to take a counterclockwise arrow symbol, \circlearrowleft from the amsmath package, and then scale, rotate, and align it. This produces a nice-looking \oint whose circular arrow can be made as large as you like; however, you have to adjust the scaling and aligning parameters correspondingly.
In the following code, you can adjust the integral in several ways. \rotatefactor is the amount, in degrees, that the symbol was rotated; and \scalefactor indicates how much it was scaled. If you adjust these, you'll have to play with \raiseamt, which controls the vertical location of the arrow, and \leftamt, which controls its horizontal location.
\usepackage{amsmath} % for \circlearrowleft
\usepackage{rotating} % for \rotatebox
\usepackage{graphicx} % for \scalebox
\newcommand{\scalefactor}{1.55}
\newcommand{\rotatefactor}{-73}
\newcommand{\raiseamt}{0.7em}
\newcommand{\leftamt}{-1.22em}
\newcommand{\bigoint}{%
\raisebox{\raiseamt}{%
\rotatebox{\rotatefactor}{%
\scalebox{\scalefactor}{\(\circlearrowleft\)}%
}%
}%
\hspace{\leftamt}\int\limits}
Then, in your document, the following code
\[
3+\ointctrclockwise_C \frac{z}{2z+3}\,dz
\quad\mathrm{versus}\quad
3+\bigoint_C \frac{z}{2z+3}\,dz
\]
produces

If this is too big, too small, etc., just fiddle with the parameters.
Things I don't like about this solution: (1) the arrow itself is kind of thick. Perhaps just replacing the head with a scaled ^ symbol would suffice; such a solution could use the same approach as this one. (2) I feel like the spacing isn't perfect; the fraction is too close to the integral. I guess this is kind of unChartered territory, though.
mathdesigndefines that integral withDeclareMathSymbol(inmdbch.sty) so it's just what's defined in the font. But you could try making your own version by combining the normal integral with a circular arrow if you can find one you prefer. – Thruston Apr 10 '15 at 10:48md-chrmb.pfbin your system, open it byfontforgeprogram, find the characteranticlockwisecontintegraldisplay, edit this character and generate newmd-chrmb.pfbfor your personal use. – wipet Apr 10 '15 at 12:09