Could a black hole maintain a stable orbit around the Earth?

Could a rotating Black Hole of mass $1.24\times 10^{10}$ kg maintain a stable orbit around Earth, without significantly altering the path of the Earth or Moon? In addition to this, would the presence of the hole have an effect on the Earth's tides?

• 1. Why that specific mass? 2. The stability of the orbit (and, in fact, almost all of the physics away from the Schwarzschild horizon) doesn't depend on the thing being a black hole at all. – ACuriousMind Apr 26 '16 at 19:31
• The mass corresponds to other calculations pertaining to its energy output. It would be an upper limit on the mass. – Noah P Apr 26 '16 at 19:35

If this object were in low earth orbit (400km altitude), then the relative tidal effects on the surface when it is overhead would be about $\frac{m_{\text{object}}}{m_{\text{moon}}} (\frac{d_\text{moon}}{400\text{km}})^3$ or a bit more than one ten-thousandth that of the moon.