Add an input field where you can enter any text:
Manipulate[ Graphics[ Table[Rotate[ Rotate[Translate[ Text[Style[text, s, FontFamily -> "Times"]], {d, 0}], a \[Degree]], i 72 \[Degree], {0, 0}], {i, 1, 5}], PlotRange -> 2], {{d, 1, "distance"}, -2, 2}, {{a, 0, "rotation"}, 0, 360}, {{s, 200, "size"}, 0, 400}, {{text, "a", "text"}} ]
With that kind of input field, you have to put quotes around what you type to indicate that it’s text (and not a symbol). Make the input field automatically treat what you type as text so you don’t need to type the quotes:
Manipulate[ Graphics[ Table[Rotate[ Rotate[Translate[ Text[Style[text, s, FontFamily -> "Times"]], {d, 0}], a \[Degree]], i 72 \[Degree], {0, 0}], {i, 1, 5}], PlotRange -> 2], {{d, 1, "distance"}, -2, 2}, {{a, 0, "rotation"}, 0, 360}, {{s, 200, "size"}, 0, 400}, {{text, "a", "text"}, InputField[#, String] &} ]
Manipulate[ Graphics[ Table[Rotate[ Rotate[Translate[ Text[Style[text, s, FontFamily -> "Times"]], {d, 0}], a \[Degree]], i 72 \[Degree], {0, 0}], {i, 1, 5}], PlotRange -> 2], {{d, 1, "distance"}, -2, 2}, {{a, 0, "rotation"}, 0, 360}, {{s, 200, "size"}, 0, 400}, {{text, "a", "text"}, InputField[#, String] &} ]