We analyze an optical atomic clock using two-photon
5
S
1
/
2
→
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J
transitions in rubidium. Four one- and two-color excitation schemes to probe the
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3
/
2
and
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5
/
2
fine-structure states are considered in detail. We compare key characteristics of Rb
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and
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/
2
two-photon clocks. The
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clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the
10
−
13
/
τ
(
s
)
-level, with integration time τ in seconds, and a relative accuracy of
∼
10
−
13
. We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb
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-states.