  The standard formation theory of binary millisecond pulsars (BMSPs) predicts
efficient orbital circularization due to tidal interaction during the previous
mass transfer phase. Therefore, BMSPs are expected to have a circular orbit.
However, the discovery of several eccentric BMSPs (eBMSPs) with a white dwarf
(WD) companion has challenged this picture. In particular, recent observation
reveals that the spin angular momentum of the eBMSP J0955$-$6150 is tilted at
an angle $>4.8^{\rm \degree}$ from the orbital angular momentum. This is the
first time that a tilt angle is deduced for eBMSPs, which provides an important
clue to their formation mechanism. Both the orbital eccentricity and tilt angle
could be qualitatively accounted for by asymmetrical mass ejection during
thermonuclear flashes from proto-WDs (so-called the thermonuclear rocket
model), but detailed studies are still lacking. In this paper, we simulate the
impact of the kick caused by asymmetrical mass ejection on the properties of
BMSPs. We find that the thermonuclear rocket model can potentially explain the
observational characteristics of both eBMSPs and normal BMSPs under reasonable
input parameters. In addition, our results predict a wide range of the orbital
period (from less than one day to more than several hundred days) for eBMSPs,
which can be tested by future observations.
