We present photometric and spectroscopic observations of the Type Icn supernova (SN) 2021ckj. This rare type of SNe is characterized by a rapid evolution and high peak luminosity as well as narrow lines of highly ionized carbon at early phases, implying an interaction with hydrogen- and helium-poor circumstellar matter (CSM). SN 2021ckj reached a peak brightness of ~-20 mag in the optical bands, with a rise time and a time above half maximum of ~4 and ~10 days, respectively, in the g and cyan bands. These features are reminiscent of those of other Type Icn SNe (SNe 2019hgp, 2021csp, and 2019jc), with the photometric properties of SN 2021ckj being almost identical to those of SN 2021csp. Spectral modeling of SN 2021ckj reveals that its composition is dominated by oxygen, carbon, and iron group elements, and the photospheric velocity at peak is ~10000 km s-1. Modeling the spectral time series of SN 2021ckj suggests aspherical SN ejecta. From the light curve (LC) modeling applied to SNe 2021ckj, 2019hgp, and 2021csp, we find that the ejecta and CSM properties of Type Icn SNe are diverse. SNe 2021ckj and 2021csp likely have two ejecta components (an aspherical high-energy component and a spherical standard-energy component) with a roughly spherical CSM, while SN 2019hgp can be explained by a spherical ejecta-CSM interaction alone. The ejecta of SNe 2021ckj and 2021csp have larger energy per ejecta mass than the ejecta of SN 2019hgp. The density distribution of the CSM is similar in these three SNe, and is comparable to those of Type Ibn SNe. This may imply that the mass-loss mechanism is common between Type Icn (and also Type Ibn) SNe. The CSM masses of SN 2021ckj and SN 2021csp are higher than that of SN 2019hgp, although all these values are within those seen in Type Ibn SNe. The early spectrum of SN 2021ckj shows narrow emission lines from C II and C III, without a clear absorption component, in contrast with that observed in SN 2021csp. The similarity of the emission components of these lines implies that the emitting regions of SNe 2021ckj and 2021csp have similar ionization states, and thus suggests that they have similar properties as the ejecta and CSM, which is also inferred from the LC modeling. Taking the difference in the strength of the absorption features into account, this heterogeneity may be attributed to viewing angle effects in otherwise common aspherical ejecta. In particular, in this scenario SN 2021ckj is observed from the polar direction, while SN 2021csp is seen from an off-axis direction. This is also supported by the fact that the late-time spectra of SNe 2021ckj and 2021csp show similar features but with different line velocities.