Overview
IND-CPA Security $\not\Rightarrow$ 1-Circular Security.
The short answer
It is quite easy to show that IND-CPA security does not imply 1-circular security. Take any IND-CPA secure scheme $\Pi := ( \Gen, \Enc, \Dec)$ and construct a new scheme $\Pi’ := (\Gen, \Enc’, \Dec)$. On input the secret key $sk$, the encryption scheme $\Enc’$ outputs $sk$; otherwise computes $\Enc(\cdot)$ on the message.
The modified scheme is still IND-CPA, but its 1-circular security is completely broken.
A few details
The algorithm $\Enc’$ takes in input only the public key $pk$, so how can it behave differently when it receives $sk$ as input? The trick here is to run $\Dec$, since it is a public algorithm as well, to check whether $m = sk$.
Indeed, compute $c \samples \Enc(pk, r)$, for a random message $r$ and then run $r’ := \Dec(pk, sk:=m, c)$. If $r = r’$ we assume that $m$ is the secret key!
Note: To minimize the possibility of making a wrong assumption, we can run many times the protocol described above.