score:5

Accepted answer

For both startAngle and endAngle, you'll have to add a quarter of a circumference, which is Math.PI/2:

.startAngle(function(d) { return d.startAngle + Math.PI/2; })
.endAngle(function(d) { return d.endAngle + Math.PI/2; });

Here is a demo snippet with your code:

var screenWidth = window.innerWidth;
//          var color = d3.scale.category20c();

            var margin = {
            left: 25,
            top: 25,
            right: 25,
            bottom: 25
            },
            width = Math.min(screenWidth, 600) - margin.left - margin.right,
            height = Math.min(screenWidth, 600) - margin.top - margin.bottom;

            //The start date number and end date number of the months in a year
            var month_space = "\x09\x20\u00A0 ";
            var monthData = [{
                month: "T"+month_space+"E"+month_space+"X"+month_space+"T"
                }, {
                month: "T"+month_space+"E"+month_space+"X"+month_space+"T"+month_space+"1"
                }
            ];

            var svg = d3.select("#chart").append("svg")
            .attr("width", (width + margin.left + margin.right))
            .attr("height", (height + margin.top + margin.bottom))
            .attr("class", "wrappersvg")
            .append("g").attr("class", "wrapper")
            .attr("transform", "translate(" + (width / 2 + margin.left) + "," + (height / 2 + margin.top) + ")");

            //Creates a function that makes SVG paths in the shape of arcs with the specified inner and outer radius 
            var arc = d3.svg.arc()
            .innerRadius(width * 0.9 / 2)
            .outerRadius(width * 0.9 / 2 + 50)
						.startAngle(function(d) { return d.startAngle + Math.PI/2; })
						.endAngle(function(d) { return d.endAngle + Math.PI/2; });

            //Creates function that will turn the month data into start and end angles
            var pie = d3.layout.pie()
            .padAngle(0.02)
            .value(function(d) {
                return 180;
            }).sort(null);

            //Draw the arcs themselves
            svg.selectAll(".monthArc")
            .data(pie(monthData))
            .enter().append("path")
            .attr("class", "monthArc")
            .attr("id", function(d, i) {
                return "monthArc_" + i;
            })
            .attr("d", arc);

            //Append the month names within the arcs
            svg.selectAll(".monthText")
            .data(monthData)
            .enter().append("text")
            .attr("class", "monthText")
            .attr("x", 0) //Move the text from the start angle of the arc
            .attr("dy", 36) //Move the text down
            .append("textPath")
            .attr("text-anchor", "middle")
            .attr("startOffset",function(d,i){return "26%";})
            .attr("xlink:href", function(d, i) {
                return "#monthArc_" + i;
            })
            .text(function(d) {
                return d.month;
            });
body {
                font-family: sans-serif;
                margin-top: 25px;
                font-size: 18px;
            }

            .monthArc {
                fill: #cc3333;
            }

            .monthText {
                fill: #FFF;
                font-size: 34px;
                font-weight: 500;
            }
<script src="https://d3js.org/d3.v3.min.js"></script>
<div id="chart"></div>


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