We solve the three-dimensional time-dependent Schr\"{o}dinger equation for a
few-cycle circularly polarized femtosecond laser pulse interacting with an
oriented target exemplified by an Argon atom, initially in a 3px or
3py state. The photoelectron momentum distributions show distinct
signatures of the orbital structure of the initial state as well as the
carrier-envelope phase of the applied pulse. Our \textit{ab initio} results are
compared with results obtained using the length-gauge strong-field
approximation, which allows for a clear interpretation of the results in terms
of classical physics. Furthermore, we show that ionization by a circularly
polarized pulse completely maps out the angular nodal structure of the initial
state, thus providing a potential tool for studying orbital symmetry in
individual systems or during chemical reactions