smooth spline through airfoil coordinates

After permuting the points so that the cusp is the first point (just like in Gypaets's answer), the methods of this answer can be used:

airfoil = Flatten[MapAt[Most @* Reverse, DeleteCases[Split[Drop[
                  Import["http://m-selig.ae.illinois.edu/ads/coord/n64015.dat"], 3],
                  # =!= {} && #2 =!= {} &], {{}}], 1], 1];

(* Lee's method, http://dx.doi.org/10.1016/0010-4485(89)90003-1 *)
parametrizeCurve[pts_List, a : (_?NumericQ) : 1/2] := 
    FoldList[Plus, 0, Normalize[(Norm /@ Differences[pts])^a, Total]] /;
    MatrixQ[pts, NumericQ]

tvals = parametrizeCurve[airfoil];
m = 3; (* degree of the B-spline *)
(* knots for interpolating B-spline *)
knots = Join[ConstantArray[0, m + 1], MovingAverage[ArrayPad[tvals, -1], m],
             ConstantArray[1, m + 1]];
(* basis function matrix *)
bas = Table[BSplineBasis[{m, knots}, j - 1, tvals[[i]]],
            {i, Length[airfoil]}, {j, Length[airfoil]}];
ctrlpts = LinearSolve[bas, airfoil];

Graphics[{{Directive[AbsoluteThickness[3], ColorData[97, 1]], 
           BSplineCurve[ctrlpts, SplineDegree -> 3, SplineKnots -> knots]},
          {AbsolutePointSize[5], Point[airfoil]}}, Axes -> None, Frame -> True]

Replace BSplineCurve[] with BSplineFunction[] if needed.

In an airfoil you probably want a sharp trailing edge and a rounded leading edge. Therefore I would choose the trailing edge as first and last point for your spline:

path = "http://m-selig.ae.illinois.edu/ads/coord/n64015.dat";
airfoilData = Drop[Take[Drop[Import@path,3], 53], {27}];
upperSide = airfoilData[[1 ;; Length@airfoilData/2]];
lowerSide = airfoilData[[Length@airfoilData/2 + 1 ;; -1]];
airfoilDataOrdered = Reverse@upperSide~Join~lowerSide[[2 ;; -1]];

Create spline:

f = BSplineFunction[airfoilDataOrdered];

Plot:

ListPlot[{airfoilDataOrdered, f /@ Range[0, 1, 0.01]}]

EDIT 1

To go through the points you can do a parametric interpolation.

f2 = Interpolation[Table[{i, airfoilDataOrdered[[i]]}, {i, Length@airfoilDataOrdered}],
                   Method -> "Spline", InterpolationOrder -> 5];
ParametricPlot[f2[x], {x, 1, Length@airfoilDataOrdered}, 
               PlotRange -> {{0, 0.03}, {-0.03, 0.03}}]

The nose should now be ok.

EDIT 2

Polar approach:

iPoints = 
  Table[{π - ArcTan[-airfoilDataOrdered[[i, 1]] + 1/4, airfoilDataOrdered[[i, 2]]], 
         airfoilDataOrdered[[i]] - {1/4, 0}}, {i, Length@airfoilDataOrdered}];
iPoints[[-1, 1]] = 2 π;
f3 = Interpolation[iPoints, Method -> "Spline", InterpolationOrder -> 2];
ParametricPlot[f3[x], {x, 0, 2 π}, PlotRange -> All]