Can quantum tomography helps to reconstruct the state? How is this possible with arbitrary quantum state? For example if I have a $$|\psi\rangle= (0.24506+0.9633i)|0\rangle + (0.0046238+0.10943i)|1\rangle$$ if I measure it will give either 1 or 0, How can I reconstruct a state using tomography using Qiskit?
If you have just one copy of the (unknown) state, you cannot perform QST to reconstruct the state. For this, you will need many copies.
As a matter of fact, there is Holevo's theorem which, loosely speaking, states that you cannot extract more than one bit of information out of a single qubit. To describe the state of a qubit you need considerably more bits, so that's impossible (unfortunately - this is one of the most restrictive theorems in the whole of quantum computing).
If you are able to prepare many different copies of the state (not necessarily at the same time), then you can perform state tomography. To learn how to do this with qiskit, check for instance their excellent tutorial on QST.