Try this

Clear["Global'*"]
u0 = 1.25710^(-6); (*Permiability of free space*)
Ic = 1.5; (*Current in amps*)
R = .15; (*Radius in meters*)
ymax = 2.5*R;
zmax = 2.5*R;
? = 4?*10^(-7); B = ? Ic/(2R); Bz[0, 0];
Bx[y_?NumericQ, z_?NumericQ] := ? Ic/(4?) NIntegrate[((z R Cos[?])/(R^2+y^2-2y R Sin[?]+z^2)^(3/2)),{?,0,2?}] (*Integral for Biot-Savart Law along the x-axis. This will equal 0. Prove it*)
By[y_?NumericQ, z_?NumericQ] := ? Ic/(4?) NIntegrate[((z R Sin[?])/(R^2 + y^2 - 2y R Sin[?] + z^2)^(3/2)), {?, 0, 2 ?}] (*Integral for Biot-Savart Law along the y-axis*)
Bz[y_?NumericQ, z_?NumericQ] := ? Ic/(4?) NIntegrate[((R^2 - y R Sin[?])/(R^2 + y^2 - 2y R Sin[?] + z^2)^(3/2)), {?, 0, 2 ?}] (*Integral for Biot-Savart Law along the z-axis*)
p1 = StreamPlot[{By[y, z], Bz[y, z]}, {y, -ymax, ymax}, {z, -zmax, zmax}]