  Self-interacting dark radiations (SIdr) can have significant implications in
the evolution of the universe, affecting the cosmic microwave background (CMB)
and the clustering of large-scale structures. In this work, we analyze the
implications of SIdr on the CMB power spectrum and explore its potential in
resolving the Hubble tension. SIdr exhibits two distinct behaviors based on the
interacting strength: strongly self-coupled and medium self-coupled. These
behaviors are evident in the analysis of CMB data. According to Planck data,
the dark radiation component consists of both free-streaming neutrinos and
possible SIdr. The total contribution from these components yields relativistic
species with $N_{\rm eff}=3.046$. In the framework of universal coupling
between dark radiations, a consistent value of $N_{\rm
eff}=3.27_{-0.31}^{+0.23}$ is obtained. Additionally, this coupling results in
an increase in the Hubble constant ($H_0$) to $70.1_{-1.6}^{+1.3},
\text{km/s/Mpc}$. However, when considering the number of free-streaming
neutrinos as a parameter, the existence of SIdr is not supported. This makes
its fraction in radiation to be $R_x=0.047^{+0.025}_{-0.053}$. Although the
Hubble constant is still enhanced, it comes at the expense of a higher $N_{\rm
eff}=3.52\pm0.25$. Our findings reveal that the ACT and SPT data provide
support for the presence of SIdr, particularly when considering a variable
number of free-streaming species. In this case, SIdr accounts for approximately
12.7\% of the total radiation content. However, it is important to note that
relying solely on SIdr is insufficient to completely resolve the Hubble
tension. Finally, we investigate the constraints on SIdr imposed by future
experiments, which improve the limits on scaled interacting strength
$\log_{10}\tilde G_{\rm eff}$ by a factor of 4.5 compared to the current
constraints.
