Can we estimate effective population size from DNA sequence data (CR or cytB sequence)?
It sure is possible.

Very simple model

It is often hard to decompose the effective population size $Ne$ from the mutation rate $\mu$ though. But it is quite common to estimate $N\mu$. For example, it is a classical result from coalescent theory assuming a single panmictic population of constant size and no selection (and a few other assumptions) that

$$N\mu = \frac{S}{\sum_{i=0}^{k-1} \frac{1}{i}}$$

, where $S$ is the number of segregating sites and $k$ is the number of sampled individuals.

More advanced models

You will probably want a slightly more advance model though.

There exist a number of estimators including Colony2, CoNe, Estim, MLNe, ONeSAMP, TMVP and LDNe. I recommend having a look at Gilbert and Whitlock (2015) who compares these estimators under different demographic scenario.