Yes, but it can be some work. You should be able to Google for guides on the subject. Note that today, it also applies to HDDs, too.
SSDs, and new HDDs, will be set up with their smallest chunks for writing or reading as 4KB, where it used to be 512B for HDDs. Your FS defaults to using 4KB blocks. Using 512B sectors, a 4KB block that crosses over multiple sectors will result in an additional sector read or write per access.
Code:
SSD or AF HDD: * * * * * * * *|* * * * * * * *|...
512B MBR : xxxxxxxxxxxxx|* * * * * * * *|...
Ideal : xxxxxxxxxxxxx |* * * * * * * *|...
*: 512B
|: sector/block/cluster boundary
xx: important MBR data that you leave alone
The default alignment, starting the first partition at 512B sector 63, results in every read or write needing to affect 1 more disk sector for every data block the OS/FS works with.
So, you would need to clone the partition aligned, then fix the bootloader. You should be able to find guides on doing it in various ways,
but make sure they are newer ones, if they use partitioning utilities, like GParted. I don't know about all of them, but GParted now has a checkbox for alignment, and defaults to either 1MB or 2MB aligning. Guides from maybe 2010 are probably much more complicated than is necessary, today.
If you use Windows 7, all you'll want to do after that is turn off Superfetch, and maybe indexing. With older versions, you'll want to disable defragging, too (7+ will not defrag SSDs).