By default, yes, people can tell that you have looked at their profile. LinkedIn puts your photo and your name on the profile page of people you view.
However, you can change this setting.
Here is the path: LinkedIn>>Photo top-right corner>>Privacy and Settings>>Select what others see when you’ve viewed their profile>>
“You name and headline”
“Anonymous profile characteristics such as industry and title”
“Totally anonymous”
Here is a more detailed set of directions.
Step 1: Sign into to LinkedIn.
Step 2: Hold your cursor over the image in the upper right-hand corner of the page and you will see a drop-down menu.
Step 3: Click “Privacy and Settings.”
When land on the Account Settings page, you will see this set of options:
Privacy Controls
Turn on/off your activity broadcasts
Select who can see your activity feed
Select what others see when you’ve viewed their profile
Select who can see your connections
Change your profile photo & visibility »
Show/hide “Viewers of this profile also viewed” box
Step 4: Click “Select what others see when you’ve viewed their profile.”
You will these options.
“You name and headline”
“Anonymous profile characteristics such as industry and title”
“Totally anonymous”