We present details of materials synthesis, crystal structure, and anisotropic magnetic properties of single crystals of CeAlGe, a proposed type-II Weyl semimetal. Single-crystal x-ray diffraction confirms that CeAlGe forms in noncentrosymmetric I4$_1$md space group, in line with predictions of non-trivial topology. Magnetization, specific heat and electrical transport measurements were used to confirm antiferromagnetic order below 5 K, with an estimated magnon excitation gap of $Delta$ = 9.11 K from heat capacity and hole-like carrier density of 1.44 $times$ 10$^{20}$ cm$^{-3}$ from Hall effect measurements. The easy magnetic axis is along the [100] crystallographic direction, indicating that the moment lies in the tetragonal $it{ab}$-plane below 7 K. A spin-flop transition to less than 1 $mu_B$/Ce is observed to occur below 30 kOe at 1.8 K in the $M(H)$ ($bf{H}|bf{a}$) data. Small magnetic fields of 3 kOe and 30 kOe are sufficient to suppress magnetic order when applied along the $it{a}$- and $it{c}$-axes, respectively, resulting in a complex $it{T-H}$ phase diagram for $bf{H}|bf{a}$ and a simpler one for $bf{H}|bf{c}$.
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