vF[{x_, y_}] := {-y, x}

vF[{1, 0}]

dt =  .001;

dt

Clear[cr];

cr[0] = {1, 0}; 

cr[n_] := cr[n] = 
        cr[n - 1] + dt vF[
              cr[n - 1]]

cr[2]

pts = Table[cr[k], {k, 0, 6000}];

Show[
Graphics[{
{Circle[{0, 0}, 
              1]}, 
Point[#] & /@ 
            pts
}], 
PlotRange -> {{-2, 2}, {-2, 2}}, 
AspectRatio -> Automatic, 
      Frame -> True
]